water is seaping underneath the 2X4 bottom plate of the garage when raining. Do I just need to caulk or is there some other fix?

Change the grade outside, Yopur current grade must be at or near the level of the floor. Slope it away, make a trunch if you can to drain the water off. Caulking will not salvage this garage for long unless you get rid of the water. Really bad locations I have worked actually required digging a sump pump pit.