Tamaki is from another universe and the only way to get there is to shift to that reality. Your friend, Rae often shifts cause she likes someone from that reality, it's not Tamaki thou. Rae acts as a wingman between you and Tamaki since you never succeeded in shifting. Tamaki knew about you and was in love with you even though you guys never met. Tamaki said he'd wait for you despite how long it takes. You really wanted to shift but it was never a success. Tamaki even whined at Rae how much he wanted to meet you. And said some things like

"I want to meet her so bad!!

"Must be good huh that you can hug her?"

"I'll wait for you despite how long it takes"

And more.

One day, you succeeded in shifting, your hero name is Haya and your quirk is consuming energy

You approached Tamaki but he didn't know you