The Ottomans didn't block the spice trade. This has been addressed in an earlier post by u/terminus-trantor here. At the time of the voyages of discovery the Ottomans didn't even control the territory through which most of the spice trade flowed (Syria and Egypt), and even if they had, Ottoman policy was not designed to block trade, but rather the exact opposite: to facilitate it. The Ottomans even granted Venetian traders the opportunity to trade in Ottoman ports at reduced taxation rates. The voyages of discovery didn't have much to do with the rise of the Ottomans in particular, but insofar as they were motivated by the status of the eastern trade routes they stemmed from the fact that for centuries prior that trade had been under the control of various Muslim regimes on land and Italian (and above all Venetian) traders by sea. The "Rise of the Ottomans -> Voyages of Discovery" link is essentially an easy way for instructors to connect together two major events in world history in order to create better narrative flow, but this link is often greatly exaggerated and explained in misleading ways.