Quicker leaven?

These are my thoughts.

Water and flour mix which activates the amylase enzymes. The amylase convert the starch in the flour to sugars (maltose and fructose). The bacteria and yeast in your starter now have food and they respond by digesting the sugars, leaving behind various byproducts (acids, flavors) and carbon dioxide. They also reproduce and create new and energized cultures.

You can develop a sort of "starter on steroids" if you feed it as often as it will take it. In other words, feed at 100%, ferment until doubled, discard some and do it again and again. The problem is the starter really never ripens and remains on the sweet side of the sweet/sour spectrum.

You might get that energized starter you are looking for but it won't be very mature, and the acids that affect how the starter performs will likely be underdeveloped. The lack of acid may favor the propagation of bacteria and yeast that are not helpful in fermentation, but instead compete for the available nutrition just the same.

Making good bread using an effective sourdough culture takes time, at least that has been my experience. As an option you could use yeast instead of a levain. Yeast is designed for fast action.

So many "it depends on..."

Starter:

Is your starter stiff or loose?

Flour based? Which flour? 

Fruitwater based? 

How is it maintained and how active is it?

Levain:

What room temp is it at overnight?

Is it maintained at a particular temp-as in a proofing box of some kind?

What temp is the liquid at that was used?

There are so many ways to make and maintain a starter so there is not enough info in your original post. What you are asking is eminently do-able and you will get a lot of opinions and info but more info as to where the starter is starting from is needed.

It can be done! You need a very active starter and the levain mixed with warm water and kept in a steadily warm (80F) environment prior to use.