How are those beams
(the long board that the joists connects to, sometimes called a rim joist) attached to the post ? Nails or lag bolts are inviting failure. Through bolts are better, but not best
They should be "set in" to the post. Also those beams should be a a couple of sizes larger than the joists, like 2x10 or 2x12 depending on the distance between the posts and the load you are going to have on your mezzanine.
If you don't want to start over with a larger, inset beam, take a 2by the width of the post and force it between the bottom of the beam and the floor, assuming you have a concrete floor. Plain wood should not rest on concrete, so cut a chunk of PT and put it between this post "add-on" and the floor.
Because your beam is so undersized, I would also add a post mid way between the 2 existing posts. Cutting the span in half will make a huge difference in the load capacity.
This is all "seat of the pants" and it still probably would not pass a building inspection.