You can retrieve messages in Gmail from other accounts using POP3, but as janusz said POP3 is an “on demand” service so you won’t get the messages immediately. When you set this up in your Gmail settings a default POP3 import interval of about an hour is used, and Gmail will then automatically change the import interval depending on how many messages are found during each import.
https://support.google.com/mail/answer/21289
If you use forwarding the messages should arrive nearly immediately (within a minute or so). However, forwarding breaks SPF and some other email reputation checks, so you may get worse spam filtering (or false positives) when you use message forwarding.
Bill