As blockchains begin processing significant economic activity, the ability to include and order transactions inevitably becomes highly valuable, a concept known as Maximal Extractable Value (MEV). This makes effective mechanisms for transaction inclusion and ordering, and thereby the extraction of MEV, a key aspect of blockchain design. Beyond traditional approaches such as ordering in a first-come-first-serve manner or using priority fees, a recent proposal suggests auctioning off a time advantage for transaction inclusion. In this paper, we investigate this time advantage mechanism, focusing specifically on arbitrage opportunities on Automated Market Makers (AMMs), one of the largest sources of MEV today. We analyze the optimal strategy for a time-advantaged arbitrageur and compare the profits generated by various MEV extraction methods. Finally, we explore how AMMs can be adapted in the time advantage setting to capture a portion of the MEV.