Refresh is a really interesting thing to happen to a character, and it'd be awesome to have that happen faster early on - by my experience, it takes a couple of weeks before first refresh.

What if at character creation, you got 1 Strength card, 1 Weakness and 1 Wild each.

At first refresh, you pick up your 2 S, 1 W, where the new S card is a copy of any of the cards you played (so you could have more of your starting S, or more of your Wild S.)

At second refresh, you take 2 S, 2 W, and so on, alternating a new S and new W each refresh.

For a more radical approach, make Wild cards completely wild - choose S/W when you play, and that's which way you grow, so when you play Wild you're saying "I want more of this..." - and characters could become unbalanced in interesting ways.

The final refinement there would be that you grow opposite to your Wild play - so if you Wild Strong, you go Weak and vice versa.