I would wager around a year at max. Most materials related to Distributed Systems are information heavy(requiring you to read and remember) as opposed to being math heavy(with the possible exception of graph theory, which usually none of the fundamental texts expect the readers to know). Even many popular papers like raft, paxos, chubby, BitTorrent, gfs etc do not require much mathematical knowledge beyond basic arithmetic. You can read them like a non-fiction and understand most of the things.
Not saying that Distributed Systems is easy, doing research in Distributed Systems is very challenging, but I don’t think reading and understanding these materials should be that difficult for an average software engineer.