If you have a purchase financing arrangement which does not require escrow, which is unlikely in your situation as a first time buyer, but might to apply to others reading this thread, then the answer is no, you do not need to pay the taxes up front for the year. This would apply to purchase using an equity line of credit (HELOC) or a cash purchase. In that situation, there is no requirement to escrow the taxes and insurance, they remain your personal responsibility, the same as any other bill. So in that situation, the only adjustment at the Closing is reimbursement to the seller for any advance periods they have already paid.
The exact amount can only be calculated on the day of Closing, and it is normally agreed with the seller that they will accept a personal check from you up to a certain amount to cover that refund to the seller, normally no more than $500, but there is no set amount.