Actually, you don't have to believe in reincarnation to be a Buddhist. There's no creed at all. It's about "come and see for yourself".

So since most of us can't see our past and previous lives for ourselves, then - there is no value really in affirming a belief in rebirth as if you knew for sure.

But - at the same time, it's going too far in the other direction to say that this life is all that there is - that's also closing off certain directions saying "I won't look that way as I'm sure there is no point, there can't be anything there".

The best for a Buddhist following the path is to have an open mind about what happens when you die.

But - there's a difference between what you see for yourself, and teachings you can listen to and contemplate. So - the Buddhist tradition is full of many teachings about past and future lives. But you don't have to believe those as a creed, there's no value in that.

There are lines of reasoning that can lead you to think that it makes better sense than many other ideas to think in terms of past and future lives. But that varies also from person to person, some find them very convincing and others don't know what to make of them or they don't mean much at all.

So, when I first heard the idea it made so much sense of so many things that had puzzled me before that I came to believe it pretty quickly, like it makes a lot of sense to me.

But not in the sense of saying I'm sure of it. Just that it made a lot of sense. So, it's like my default assumption. Nothing wrong with that. We all have many default assumptions, e.g.  lots of assumptions about the world we are in, what kinds of creatures we are, about our universe and so on. So it's like that. I can't prove it. Maybe if I'd been brought up different I'd have believed in ancestor worship, or an afterlife or whatever.  I think for many traditional Buddhists it may well be like that, not something you think about much at all, but you just have it as background, that this is what makes most sense to you so you tend to go along with it, in absence of any reason to use some other world view.

Different Buddhist traditions vary in how much emphasis they give to ideas of reincarnation, but it is present in them all I think except for some modern secular  versions of Buddhism which try to reinterpret the original teachings of the Buddha without the idea.

But as far as following the path of the Buddha, really, the main thing you need is just an open mind about what happens when you die, as it is about awakening to the truth, whatever it is, as it is, rather than trying to fit it into preconceptions.