Without getting into the math too much, it usually doesn't make sense to exercise an option, which has any time premium over intrinsic value. For most options, that doesn't occur until close to expiration. Think about the result of an exercise. An investor who exercises a put uses it to sell shares and receive cash. A person exercising a call option uses it to buy shares and must pay cash.
People are more likely to exercise options if it means they can receive cash sooner.
The opposite is true for calls, where exercise means you have to pay cash sooner. OCC randomly assigns exercise notices to Clearing Members in whose accounts have short positions of the same series. The Clearing Member then assigns the exercise to one of its short positions using a fair assignment method, though not necessarily random. You should ask your brokerage firm how it assigns exercise notices to its customers. No, it is not possible.