Do not tolerate and do NOT IGNORE! If you address it while it's small, it won't get worse. This is totally normal for him to be trying. Address it right away when he does it every time with a consequence so he learns not to do it.
Telling a 2 and 1/2 year old it "isn't very nice" is fine for your own gratification of saying something but means nothing to them. It won't stop the behavior in any way. Just calmly and firmly say, "No, no pushing" or "no hitting" with the consequence so he learns the command and the point.
If you give a consequence early on before it escalates, he will learn very quickly what is allowed and it won't become a bigger issue. He will soon follow just your calm verbal command to avoid the consequence as well as learning naturally not to hit or push with no warning from you eventually.
Footnote on the "it's not nice" thing. You don't want to try to instill guilt. It's not about his character at this age. Avoid the broad concepts involving sympathy until later. I never use the good boy/bad boy label for any reason. Well that's not true, I call him good boy all the time during praise when he's being good, but not in an explanation on "how to be a good boy". Of course he's a good boy. No name calling necessary during discipline, just instruction for actions. The simpler and briefer your approach the better for his fast learning. You basically need him to mind you and learn what you will allow.