They are not clearing out their inboxes without checking queries UNLESS they were closed to queries for a time and cleared out that came in during that time.
If an agent isn’t open to queries, they’ll tell you. Otherwise you CANNOT know when is the best time to query. There is all sorts of nonsense about “Don’t query in January, you’ll get lumped in with the people querying bad Nanowrimo novels;” “Don’t query in summer because agents are at conferences;” “Don’t query in August because publishing shuts down;” “Don’t query at the holidays because they aren’t interested right then and they’ll delete your queries unread.”
Those are ALL BULLSHIT.
Agents are either open to queries or they aren’t. If they are, query them.
There is no best time, no matter what people say.