Welcome. Neil has given you some good advice.
If you have already glued this up you will have a wicked time fitting that bottom.
I would definitely cut a pattern particularly if you are planning on using a solid wood panel (not advised) for the bottom. Use 1/4" mdf or similar to make sure I had a snug fit and perfect registration on all four sides and the legs.
In this instance I would probably go with a veneered plywood or similar as there will be less movement and it will be less likely to stress the current joinery.
If you could give us more details of the rest of the cabinet design i.e. drawers, shelves etc. We might be able to help you out of some future jams.
I think a rabbet will weaken the rails which look to be about 7/8-3/4" thick.
Depending on the weight of the items you plan to put in this case I would also think about putting some support under the bottom so it doesn't sag.
Welcome to FOG. I like the design so far.
It appears that you have aleady glued up the piece, which will make it next to impossible to add a dado or rabbet to the lower frame at this point to inset a bottom into the case. Ideally, you would run a dado around the front, back, sides to align the bottom with the top of the four bottom rails of the piece. If it is glued up, you won't be able to do that.
As an alternative, I'd rip 3/4 x 3/4 strips the full length of the rails and glue them on the insides of the bottom rails to reveal a 3/4 inset that you can then drop the bottom in and bring it flush with the top edges of the bottom rails. I'd screw it from the inside into the four rails and then drop the bottom in and screw that into the strip from the bottom.
It sounds like you are making the bottom from solid wood, so you'd glue it up and finish sand or plane it and then cut to fit and knotch the four corners where the legs are. I assume you can drop that in from the top. It's not clear if the tapered legs will allow you to insert this from the bottom easily.
You should also think about how you are going to insert the two interior sides that appear to be needed on either side of the drawers in the center unit. Normally, I build these cases from the inside out - carcase first and then end up with the outside pieces.
Those interior drawer sides will need to be mounted to the front and back frames, which looks to be a challenge given how you have built this thus far. Pocket hole screws are one alternative at this point to attach it from the interior of the drawer cabinet so they don't show in the shelf side.
Hope this helps. If I've misunderstood the question or if you have not glued up the piece, you could do the dado or rabbit for both the bottom and drawer sides now and then assemble with those in place.