What is the standard trombone mouthpiece.

Bought a cheap trombone and it came with a 7c mouthpiece that looks identical to the common trumpet mouthpiece. But it is very difficult to hit lower trombone notes, but very easy to play higher than the base clef notes.

So I did some research and it said common sizes are 7c, 6 1/2al, and 12c

The 6 1/2al and 12c look identical and both are HUGE. This is a trombone not a tuba. I feel like trombone should have something in between.

What is the correct common size that a child starting in grade school use?