Require registration BUT NOT use activation link

We have a event registration site where a number of people often try to register for the event in the same period of time (100+ in minutes and then the event is sold out).

Too often some users complain "I could not get into the event because the system did not send me the email activation link".

We do send a link (and ask them to check junk/spam folders.. screenshot) but it slows the process and seems unnecessary. Is there a way to require login + registration but have the fluid process (like a guest)?

Users definitely need to have accounts with us as we use their profiles in the event (via Community Builder).

Here is what they see now but some still do not get the activation email:

OMG. You serious? That easy? Sorry and thanks at the same time.