Kind of, but not really. There is a system that could theoretically allow it, but there are safeguards built into that system to prevent crit manipulation. The reason it theoretically works is because the game uses psuedo-RNG, which is a way of normalizing crit outcomes to limit the impact of RNG screwing someone. It does this by starting you at a lower value than your actual crit chance for your first attack, then building it up as you attack without getting crits. As an example, if I had 50% crit chance, my first attack might only have a 25% chance to crit (that is not the actual number), which then goes up by 20% every time I don't crit. I still end up with a 50% chance to crit over a large number of attacks (again, not with these example numbers), but with much less variance. Theoretically, we could use this to autoattack creeps a few times, then go all-in if we didn't get a crit on the minions because a first-hit crit on the enemy is much more likely now.
However, with the way the game actually works, you can't really get much from doing this. From what we've been told in the past, there is a mechanism in the formula to mitigate crit manipulation. This likely means that the crit chance for minions and champions is independent (so you can't build crit chance on minions), or that crit chance is independent on all targets, or that starting to crit then canceling your autoattacking to not lose your crit chance actually will burn the crit chance. We don't know exactly it is, but we do know that doing this generally has very small potential rewards, particularly as crit chance goes up and variance goes down.