Publishing is an extremely slow industry and agents will always put their clients' work first... so if they have a bunch of client manuscripts to read, they'll likely read those first.
It's definitely not unusual for agents not to confirm receipt and it's also not unusual for an agent to take several months with your manuscript. I would say it's okay to nudge after 3 months, but don't be surprised if the answer you get is something like "It's still in my to-be-read pile". (And nudging after 6 months is obviously fine, too.)
Some agents are super fast and respond to requests within a few weeks, but I would say those are an exception. Sadly, there's also a bunch of agents out there who are known to ghost authors on fulls, so I would recommend looking at the comment sections for the agents who have your material to see if that's something that could possibly happen to you.
Good luck!