If quarks are in fact made up of smaller particles, would we ever be able to find evidence for them? Disclaimer: I'm not trying to suggest that quarks are made up of smaller particles. This is just a "What if?".
We've had to infer the existence of quarks through the behavior of hadrons in particle accelerators, because the strong interaction won't let us see a quark on its own (except maybe the top quark, which has such a ridiculously short mean lifetime that it usually doesn't last long enough to join up with other quarks). Whatever elementary particles make up quarks, if they even exist, must be held together even more strongly than quarks are; otherwise, the quarks would break apart before the strong force created quark-antiquark pairs.
 A: All high energy particle experiments are trying to go beyond the standard model of particle physics, i.e find data that do not agree with the predictions of the present standard model. .Take the latest example of a discrepancy seen between predictions and data in B decays.
If this discrepancy is validated with more experiments, then the standard  model should be modified. I say "modified" because the standard model is based on an enormous number of data, any new theory should be able to predict the same behavior  as the present standard model where it fits well, and then have the extra behavior that would resolve the discrepancy.

If quarks are in fact made up of smaller particles, would we ever be able to find evidence for them?

This is the type of evidence that one can find in data indicating  new physics modeling is needed: discrepancies with the current  standard model.
Here is a thesis on preon models, which assume

2.1 What is a preon?
A preon is a theoretical particle which is an element of composite leptons or quarks.
In other words, preon models assume there’s a more fundamental kind of particle
than those we have already observed. Different preon models consider different
numbers and different natures of the preons, and this thesis will treat some of
these models

If you read it you will see that it follows the program above, have a new model that incorporates the standard model group etc behavior so that it also predicts the existing data.
