There's two options, one is to turn it into a string as discussed.

The other is:

Format a cell with a number format such as \0000. This format can be assigned in the Format code field under the Format - Cells - Numbers tab, and defines the cell display as "always put a zero first and then the integer, having at least three places, and filled with zeros at the left if less than three digits".

https://help.libreoffice.org/latest/en-US/text/scalc/guide/integer_leading_zero.html

Start with a »'«. Or configure the cell to not be a number, but a string.

Change the number format to 'Text'.

General will attempt to apply the correct format based on cell contents. The numbers are making it implicitly apply the 'Number' format to the cell.

Format Cells / Numbers (tab) Category (choose Number) / Format (is General) / Options (Leading Zeros 1)

Do not format numbers as 'Text' if you need to use them in formulas of finance like sums.

Did you try putting a ' at the start of the cell?

people already explained the options but just want to mention I just do the string thing. The only time I come across the need is for id type numbers and usually am not going to do any math on it. in that case i makes sense to treat it as a string.