Yes and no
This is what the ability gains every four levels represent: actions your character is taking to improve an ability score. Most players don’t spend a lot of time discussing why they get those gains (since it’s “obvious” why the barbarian gains more Strength or the cleric gains more Wisdom), but the function of this mechanic is precisely to model the kinds of training that you are discussing.
In general, the game leaves the description of downtime training, maintenance, and so on very vaguely defined; that is supposed to be up to the players to describe. But leveling up isn’t magic. It’s an abstraction for exactly that kind of training and practice. You are assumed to be constantly studying, or lifting, or practicing skills, or maintaining gear, and so on, during any downtime you have. It’s all abstracted away, and then at some point it “all comes together” for you, you have that eureka moment, and you level up.
(No, this system does not bear close scrutiny.)
This is an extremely slow way to gain any ability score, however, and the game’s math has it “already accounted for,” so using it to increase Strength as a wizard is, from the game’s perspective, basically the same as losing Intelligence – since the game assumes that’s where you’ll be putting it (and monster designers take the resulting save DC increase into consideration when deciding monsters’ saving throw bonuses). But you still can.
Ultimately, wizards have exceedingly little use for Strength. A handy haversack and portable hole are great items anyway, so carrying gear isn’t all that important, touch attacks are trivial in most cases anyway (and you usually prefer ranged ones, which use Dexterity). The only real problem is the risk of being rendered unable to move by Strength drain or damage.