How to use Gmail for POP from Office 365 when there are too many messages?

I have an email account in Office 365 that I want to transfer into my Gmail account. Unfortunately, the only way to do it would be to use POP (it doesn’t seem like Gmail in the web interface allows to download mail using IMAP) and the problem is that there are many emails on the account.

I get the error

Error: Too many messages to download

I don’t want to transfer all messages anyway, just the ones from a certain date, but I just don’t know how to do that in Gmail or if it is possible. Is my only solution to delete email on the POP server? I would rather not do that.

Just to perhaps help, the POP server is an Office 365 account, so maybe there is another workaround to forward email from this service to my Gmail account.