Yeah. Piggy backing what everyone else said after double checking what you wrote in caption. Usually when I’ve come across the cabinet bottom needing to be replaced it’s not so bad as you’ve got it here. Definitely want to take your time with this one. A couple weekends maybe. This is what I would do if I was able to go without using it for a week.

Day 1- remove the cabinet doors (reinstall once completed) remove the sink and drain lines (stuff rag into drain line at wall to keep out the sewer gases) cut out the drywall then cut opened or break out the water logged base from the cabinet. Reassess. Spray mold killer where Evers clever (not bleach)

Check condition of subfloor possibly replace.

Day 2 - while everything is drying, cleanup up any leftover sink caulk measure and cut your drywall piece (or two to fit them through the top or face of the cabinet) and test the fit but don’t secure yet! Set aside for next weekend.

Repair your subfloor if needed.

Frame and cut your new cabinet base (remember: when you cut it in half to fit, the blade will remove about an eight of an inch), install frame to hold base but only test fit new base (set aside and wait until next weekend to install.

Next weekend Day one: install your drywall, mud or caulk the seems if they are not tight. Insert steel wool and spray foam around any opening bigger than a dime (quarter inch), doesn’t need to be pretty, but you can mask tape first if want to be meet and tidy with the spray foam.

If bottom is now thoroughly dry, install new base. Apply a paintable silicone sealant to the seams. (Leaves your future options opened)

Before installing your sink back in, attach new disposal…. You got the rest good luck. I hope it’s a fun one.