It might be possible to run an ACME client on another host in your environment. (IMHO, the DNS-01 challenge is very useful for this.) Then you can (probably) transfer the cert+key to BIG IP, and activate it, via the REST API.
I haven’t used BIG IP in a long while, so take this with a grain of salt, but it seems to me that it might not be impossible to get something going – despite the fact that BIG IP itself doesn’t have native support for ACME.
Those tend to be quite brittle in reality. What’s the old adage about engineering vs architecture again?
Something like this I think: https://www.reddit.com/r/PeterExplainsTheJoke/comments/16141...