If you get objectives, and create pressure allowing your team to capitalize on it, then you can get some of your team mates who are better late game champions then you stand a better chance.
Shutting down the opposite team is a good strategy, making them fear leaving their base or baiting them to extend or contest dragon / baron is also good. If you and your team can get an advantage then you should have no issue with the late game.
That said when you do transition to the late game, if your champion does not perform as well as other late game champions, then maybe you can defend your more valuable teammates (like AD carry) to allow them to both live and win team fights and continue to earn and build items.
Also try not to take too much farm from your team, and try to snowball as best as possible.