If life is pointless because it's finite, it would also be the case that it is pointless to have a nice meal, to watch a movie, to play a game, to talk to people, to engage in hobbies. Why would you do any of that when you know there will come an end to the meal, to the movie, to the game, to the conversation?
But most of us engage in those things, because the point is that we enjoy it - there doesn't need to be some eternal consequences for us to enjoy it. In fact, some argue that the finitude adds more meaning to it. If you eat your favourite meal once a month, that may be really special, but if you eat it every day, it becomes somewhat boring or you might even start to hate it. Someone might really enjoy a TV series at first, but they lose interest after a few seasons. And so on. This isn't true for everyone all the time, of course, but the point is that there doesn't need to be an eternal purpose for there to be meaning.
Also, if you have an eternity to look forward to, some argue that this diminishes the meaning in whatever you do now. If you have a finite life, this is all you've got and all you can do is make the best of, so that makes it as meaningful as it could possibly be for you. If you'll life forever, anything that doesn't have eternal consequences would be less significant - if you'll have billions of years of experiences to look forward to, why would it matter to have one nice day now? If you're always trying to contextualise purpose in terms of eternity, you won't find meaning in a finite life, but you also won't find meaning in an eternal life, because you'll always be focused on the future and never on the present.
One lie religion tells us is that you need eternity to have purpose, but that claim bends and breaks when you apply even a minimal amount of scrutiny to it.
Of course, there is also the question of what gives us purpose in our finite lives.
But this is something for each individual to figure out for themselves.
Some may feel fulfilled by helping others and through relationships. Some may feel fulfilled by their career, others by their hobbies or by more hedonistic pursuits or by whatever legacy they may leave behind.
None of these are more or less valid than any other, but any one of these may be more or less fulfilling to any given person, and it's up to you to figure out what's most fulfilling to you.