Just fill the time

You already said it, It's just out of order. You move on with your life, and the getting over someone part comes later.

It's frustrating to try to force it to heal faster than it's going to and I encourage you not to rush into something faster than you should. I've been on the receiving end of that. It's not fun dating someone that's mentally dating their ex.

When the tears stop the hurt will still be there, but I'd invite you to rediscover who you were when you were single or if it's been some time. Find out who you are as an individual. Are you into the working out, writing, gaming, sports, partying, etc? You've got nothing, but time now. Fill it with something.

Voids are supposed to be filled.

Give yourself time, but make sure you're filling that time with things you enjoy. There's no deadline for your next relationship.