As far as I read, the Ottoman state was not interested in joining the colonization race, since they already controlled the trade routes to the far east.
But why were individual Ottoman pirates not intercepting gold hauling ships of colonizing nations?
They appear to be ruling the Mediterranean in the 16th century. The news of gold from the new world must have surely reached them.
Were they afraid of sailing out of the Mediterranean for some reason? Did they lack some technology? Was it due to some policy?
Your assertion that the Ottomans "controlled the trade routes to the far east" is an oversimplification of the situation in the 16th century. They controlled part of a route that was a bottleneck for trade between Europe and large parts of Asia, but they did not control the entire trade route.
Your other assertion that they were "ruling the Mediterranean in the 16th century" is also misleading. While piracy and slavery in the Mediterranean were serious problems up until the 18th century, the Ottoman simply did not ever dominate the entire Mediterranean. They were checked both in the Siege of Malta, and the Battle of Lepanto, both in the 16th century.
Further on sailing out of the Mediterranean, beyond not having control of the western Mediterranean, you may want to read several recent posts:
The conflict over Mediterranean waters was covered in several books, including:
Sometimes so-called "Turkish" pirates will show up in what seem to be the most unlikely of places. An example would be in 1631, a Basque vessel was attacked by a ship bearing a three-crescent flag, in the stretch of water between Newfoundland and Cape Breton.
What follows is an account of the incident, quoted in Ruth Holmes Whitehead's Nova Scotia: The Protohistoric Period 1500-1630.
On the eighteenth they sighted land at Cape Ray; and shortly afterwards they perceived a vessel, which they took for a Turkish one, coming down upon them with the wind. This made them get under way and prepare for defence; but the Turk, perceiving a considerable number of men on the deck, drew off and bore down on a Basque vessel at which it fired some cannon-shots and then drew alongside. The grappling was not well done, however, and the vessels separated; and, as they separated, a Basque sailor who was in the stem of his vessel grasped the flag that was in the stem of the Turk, and pulled it to himself. At once the Basque vessel began to make off ... so that it escaped and carried off the said flag, on which were depicted three crescents.
Whitehead argues that the pirate vessel likely originated from one of the Barbaray Coast States in North Africa. So while probably not Ottoman per se, it is an example of similar pirate operating outside of what would ordinarily be considered traditional territory.