You can close a small miter gap by rubbing it with a screwdriver shank or any hard, smooth tool. We used the end of a utility knife. That crushes the wood fibers inward to make the gap disappear. Even professional woodworkers sometimes resort to this crude trick.
Here's an old favorite trick among woodworkers. Clamp on notched blocks, then add a bar clamp or two to squeeze the joint. This allows you to put a lot of pressure on the joint without buying any special clamps. If you're assembling a four-sided project such as a picture frame, join two corners first. Then, after the glue has set, join the two halves of the frame.