Gosh, he might still be adjusting to 1st grade? Unless he's had some socially unpleasant experiences with peers or thinks the teacher is mean and unless he's had some form of 'uncomfortable' experience he doesn't know how to put words to, I'm thinking he might just be a bit sensitive for now. Getting in trouble for crying probably won't help.
Maybe try to have him 'succeed' in activities that require some effort to help build his self esteem and invite some of his peers over for play dates. Maybe some games that require 'messiness' and imperfection as the fun part as well.
Sometimes children adapt to change by trying to have control over things like orderliness and so forth and his intense emotions are reflecting he doesn't feel in control of things that make him feel safe. I might try putting him in charge of preparing for the day...such as today he gets to choose what kind of snack he'll look forward to having at school or he'll choose what kind of special outfit to wear. Be creative and have fun with it! He'll probably need to cry until he's ready not to so I'd maybe recommend not putting forth any judgment because that will delay his resiliency.
It might sound weird, but maybe if he feels like crying make it a scheduled thing where he gets to choose between crying or making jokes and laughing. If he chooses to cry, then that's okay and maybe he gets 5 minutes and then take the opportunity to talk about if it made him feel better...sometimes a good cry is a release! If he chooses to make jokes and laugh, then the opportunity to talk about if it made him feel better.
Many might feel what I'm saying gives too much control over to the child, but please understand where emotions are concerned, he NEEDS TO BE IN CONTROL and it is our responsibility to help our children learn to identify emotions, where they come from, why they exist, and what helps them feel better when negative emotions take over. If he can't do this right now (which isn't entirely uncommon for this developmental age!!!) then he needs to know he's not weird or doing something worthy of feeling shame over. Self confidence will help him most I believe.
Best wishes!