Great question!

So, first off, if I knew what app(s) specifically you have in mind, that'd help me answer better, but in general:

• First off, I'll say it's mostly less that they support pacman than that Arch supports them. There may be some exceptions, but it's usually Arch developers building the pacman packages rather than the author of the software in question. Even when it's a proprietary application, it's usually bundled into a packman package (or at least a PKGBUILD for it lives on AUR, but we'll get to that) by one of the Arch developers or other volunteers.
• Your first option for software that isn't in the official Arch repositories is AUR. It's for packages that aren't as officially supported as those in the official Arch repositories. Anything in AUR, you'll have to build the package itself (which usually involves compiling, unless it builds the package from an already-compiled binary), but the process is usually pretty straightforward. (Download and unzip the tarball from AUR somewhere, cd into the directory, and then makepkg -sf && sudo pacman -U <something>.tar.xz. You can also get some helper scripts that do some of those steps for you for convenience. Definitely worth having the experience of doing it manually a few times first, though, I'd say.) Even if the only way to get the software in question from the publisher is in .deb form, you may still find a package on AUR that will unpackage the .deb and package the result up into an Arch package.
• You can run the software in an isolated way. There are snap packages and flatpacks, but... well, there are good reasons why they get a bad rap. Lol. Another option is to build an Ubuntu chroot in which to install the package in there. The cleanest and most straightforward option for running software isolated like this is probably Docker. (Running graphical apps in Docker can definitely be done, though it is a little tricky.)
• You can grab the software in question and install it manually somewhere in your home directory. Somewhere like $HOME/install/<softwarename>. This can work even if the software is only available as a .deb file. You can just extract the .deb without installing it with the command ar x <blah>.deb and a tar -xf data.tar.gz and then put the files from within that .deb file where you want them.
• There are some other options that I've never tried (and only learned of just now by googling) that... aren't recommended. Here's a link for reference, but to somewhat explain the problems that those approaches there can cause, when you install a package from any particular package manager, the package manager installs dependencies. (Typically those dependencies are shared libraries. Think ".dll"s.) And those dependencies live in specific places. But if, say, you had pacman and apt-get installed on the same system and install the same dependency (including if that dependency is installed automatically as part of installing something else) via both package managers, it's likely to get one version of the dependency from one package manager and another from the other. Either one package manager is going to error out ("these files already exist in the filesystem, I think something's wrong that a human should fix") or overwrite files potentially breaking things. (Now, all that said, I know that pacman is actually in the official Ubuntu repositories and can be installed on Ubuntu alongside apt get. I have to admit I don't know if and if so how it goes about avoiding problems if both are installed. Maybe it's not a good idea to install pacman on Ubuntu for the same reason. Who knows!)
• So, there is also the option to write your own PKGBUILD. (A "PKGBUILD" is a script that tells your Arch system how to build a Pacman package. They're what you download from AUR when you want to build/install something from AUR. A couple of reference links.) It does require doing a little Bash programming, but It's not as hard as it sounds. (And it's easier than building Ubuntu packages.) I'll talk about what to do if you truly can't get the package in question anyhow except in .deb form. But first, if you can get the source code, you can typically grab a PKGBUILD from the official Arch repositories or from AUR that installs something "similar" to what you're wanting to install and modify it. (Like, for a simple example, if you're trying to install something written in C, you can look for a PKGBUILD for something written in C that would probably have similar dependencies.) If you can't get the source code but can get a compiled distribution of the software in question, you can still write a PKGBUILD, and you'll probably be able to find some PKGBUILDs to start from that would be pretty similar to what you need.
• If you truly can't get the software in question except in .deb form and you want to write a PKGBUILD for it, that can be done. It just involves writing a PKGBUILD that extracts the files from the .deb file and then packages them back up into an Arch package. I've done this before and I have a funny personal story about that. More info here in an answer to another question in this same Lemmy community.

Just in case it's useful to you, I'll share the PKGBUILD I wrote for converting the Ubuntu kernel into an Arch package. It demonstrates how you'd go about extracting files from a .deb file in order to build them into an Arch package.

pkgname='linux-ubuntu'
pkgdesc='The Ubuntu kernel, modules, and headers'
pkgver='5.15.0'
_pkgver="$(cut '-d.' -f 1,2 <<< "${pkgver}")"
_firmware_ver='1.187.29'
_suffix_ver='20.04.2'
pkgrel='25'
arch=('x86_64')
options=('!strip')
url='http://ubuntu.com/'
source=(
    'http://archive.ubuntu.com/ubuntu/pool/main/l/linux-firmware/linux-firmware_'"${_firmware_ver}"'_all.deb'
    'http://archive.ubuntu.com/ubuntu/pool/main/l/linux-hwe-'"${_pkgver}"'/linux-headers-'"${pkgver}"'-'"${pkgrel}"'-generic_'"${pkgver}"'-'"${pkgrel}"'.'"${pkgrel}"'~'"${_suffix_ver}"'_amd64.deb'
    'http://archive.ubuntu.com/ubuntu/pool/main/l/linux-hwe-'"${_pkgver}"'/linux-hwe-'"${_pkgver}"'-headers-'"${pkgver}"'-'"${pkgrel}"'_'"${pkgver}"'-'"${pkgrel}"'.'"${pkgrel}"'~'"${_suffix_ver}"'_all.deb'
    'http://archive.ubuntu.com/ubuntu/pool/main/l/linux-signed-hwe-'"${_pkgver}"'/linux-image-'"${pkgver}"'-'"${pkgrel}"'-generic_'"${pkgver}"'-'"${pkgrel}"'.'"${pkgrel}"'~'"${_suffix_ver}"'_amd64.deb'
    'http://archive.ubuntu.com/ubuntu/pool/main/l/linux-hwe-'"${_pkgver}"'/linux-modules-'"${pkgver}"'-'"${pkgrel}"'-generic_'"${pkgver}"'-'"${pkgrel}"'.'"${pkgrel}"'~'"${_suffix_ver}"'_amd64.deb'
    'http://archive.ubuntu.com/ubuntu/pool/main/l/linux-hwe-'"${_pkgver}"'/linux-modules-extra-'"${pkgver}"'-'"${pkgrel}"'-generic_'"${pkgver}"'-'"${pkgrel}"'.'"${pkgrel}"'~'"${_suffix_ver}"'_amd64.deb'
    'linux.preset'
)
noextract=(
    'linux-firmware_'"${_firmware_ver}"'_all.deb'
    'linux-headers-'"${pkgver}"'-'"${pkgrel}"'-generic_'"${pkgver}"'-'"${pkgrel}"'.'"${pkgrel}"'~'"${_suffix_ver}"'_amd64.deb'
    'linux-hwe-'"${_pkgver}"'-headers-'"${pkgver}"'-'"${pkgrel}"'_'"${pkgver}"'-'"${pkgrel}"'.'"${pkgrel}"'~'"${_suffix_ver}"'_all.deb'
    'linux-image-'"${pkgver}"'-'"${pkgrel}"'-generic_'"${pkgver}"'-'"${pkgrel}"'.'"${pkgrel}"'~'"${_suffix_ver}"'_amd64.deb'
    'linux-modules-'"${pkgver}"'-'"${pkgrel}"'-generic_'"${pkgver}"'-'"${pkgrel}"'.'"${pkgrel}"'~'"${_suffix_ver}"'_amd64.deb'
    'linux-modules-extra-'"${pkgver}"'-'"${pkgrel}"'-generic_'"${pkgver}"'-'"${pkgrel}"'.'"${pkgrel}"'~'"${_suffix_ver}"'_amd64.deb'
)
sha256sums=(
    '22697f12ade7e6d6a2dd9ac956f594a3f5e2697ada3a29916fee465cc83a34a1'
    '595794e8ad28ed130af60e6ec8699313e1935ae70f7530a00b06dff67fb4d40e'
    '22dbdc1895f91d3ad9d4c5b153352f1cc8359291dba6ea1a0e683cc6871b0f58'
    '5705cefab39dd5512bcc515918d09153715c7bb365d6bc29cc9b0580e5723eef'
    '3d207388812e957447162c067fb637b4d06eccb4f303b801e8402046a7d3cf48'
    '2f1214dbb04cb47ce8d096bff969fca9c78c26ec21a395c12922eca43cc18e26'
    '75d7d4b94156b3ba705a72ebbb91e84c8d519acf1faec852a74ade2accc7b0ea'
)

package() {
    for f in "${noextract[@]}" ; do
        ar x "${f}"
        tar -xf "data.tar.xz" -C "${pkgdir}"
    done
    rm -r "${pkgdir}"'/usr/share'
    rm -r "${pkgdir}"'/usr/lib'
    mv "${pkgdir}"'/lib' "${pkgdir}"'/usr'
    install -Dm644 'linux.preset' "${pkgdir}"'/etc/mkinitcpio.d/linux.preset'
}

(I omitted the linux.preset file. It's just in the same directory with the PKGBUILD and it gets bundled into the Arch package. But it's not really important for what you're doing unless you're trying to install a different kernel than the official Arch kernel on an Arch system.)

The part that extracts the files from the .deb packages is the ar x command and the tar -xf command. The package() function there is what decides exactly what files will be in the Arch package and where. And makepkg builds the package archive after running package().

That covers all the options for installing software not in the Arch repos that I can think of.