All you need is a PI subnet (PI = Provider Independent). There are providers that give you for example up to 5 such subnets (each a /48) for free. I use route48.org (not affiliated) but there are others.
Next, you need an ASN. You can't get these as an individual directly, but only through a sponsoring LIR (Local Internet Registry). You can find LIRs through RIPEs homepage (e.g. https://www.ripe.net/participate/member-support/list-of-memb...), I simply checked them out one after another to find out how/when/if they would sell ASN registrations to individuals. I settled with a nonprofit (IN-BERLIN e.V) that I joined, and who offer ASN registrations for a flat 50€.
Then you need a peering, usually your LIR also offers that (ask them), but you'd probably need to host your hardware in their datacenter for that to work (additional costs/month). Then there are providers like the aforementioned route48.org who allow you to peer from anywhere through a WireGuard (or GRE) tunnel, which means you can host your BGP router at home if you want (mine runs on a RaspberryPi 1st gen and has the full BGP table, which, admittedly, is a bit smaller for IPv6 than it would be for IPv4)
So yes, it's doable even for an individual, but my suggestion is to use IPv6.