Splitting strain gauge signal before amplification
If you just have the one strain gauge and you are alright with whatever gain your selected instrumentation amp affords you I would go with Andy aka's suggestion.  There are some really nice old Burr-Brown (TI bought them a long time ago) instrumentation amps for this sort of thing that have adjustable gain via a resistor and can get you a nice large scaled single-ended voltage to measure instead of the small differential voltage.  For example:

https://www.digikey.com/short/3vpvh7

If you have more than one strain gauge, or you just want more design detail control, you could instead try something like what's suggested here:

https://eewiki.net/display/Motley/Analog+Bits+-+Analog+Combinator+Circuit+for+Load+Cells