You can configure Syncthing for more ad-hoc, but it's a little convoluted.
Try Resilio Sync - it has a Selective Sync feature that allows you to select individual files to sync in the moment.
I use Resilio this way to access my files at home - Resilio runs on a machine at home and indexes/shares the root folder on my NAS. Then from any device (including my phone) I can browse for any file and select sync. It will take as long as needed for the file size and network stability, but it will sync the file.
This is especially useful for media files, since I can't exactly keep my entire library (4 TB) synced to my phone, but using Resilio I can grab any movie/TV show/music at any time.
Just don't leave Resilio running your phone - it can be hard on memory as it keeps an index there, and it isn't the most battery friendly app. So I close it when done syncing something.