In 1608 several Dutch spectacle-makers applied for patents for telescopes, most famously Hans Lippershey.
Lippershey's application for a patent was mentioned at the end of a diplomatic report on an embassy to Holland from the Kingdom of Siam sent by the Siamese king Ekathotsarot: Ambassades du Roy de Siam envoyé à l'Excellence du Prince Maurice, arrivé à La Haye le 10 Septemb. 1608 (Embassy of the King of Siam sent to his Excellency Prince Maurice, arrived at The Hague on 10 September 1608). This report was issued in October 1608 and distributed across Europe, leading to experiments by other scientists, such as the Italian Paolo Sarpi, who received the report in November, the Englishman Thomas Harriot, who was using a six-powered telescope by the summer of 1609, and Galileo Galilei, who improved the device.
Obviously several members of the Dutch spectacle making community were aware of the concept of spy glasses in 1608, since several applied for patents for them. I can imagine some of those might have made several spy glasses and tried to sell them to whoever they thought might benefit for them.
And the report of the Siamese Embassy spread news of the spy-glass around Europe so that several scientists and educated people started making them.
So publicity from either spectacle-makers in the Netherlands or scientific discoveries by Galileo and others with early telescopes would have been heard by mariners, and some would have thought of using spy-glasses at sea.
The first record of a telescope comes from the Netherlands in 1608. It is in a patent filed by Middelburg spectacle-maker Hans Lippershey with the States General of the Netherlands on 2 October 1608 for his instrument "for seeing things far away as if they were nearby". A few weeks later another Dutch instrument-maker, Jacob Metius also applied for a patent. The States General did not award a patent since the knowledge of the device already seemed to be ubiquitous but the Dutch government awarded Lippershey with a contract for copies of his design.
So what were the telescopes purchased by the Dutch government used for? When a government buys something, there is usually a bureaucratic record that provides clues to the intended use.
The OP cites several references to telescopes used at sea in 1614, 1615, and 1619 by Portuguese and Dutch sailors.
A letter from Galileo to the Doge of Venice in 1609 suggested possible military and naval uses of Galileo's new telescopes:
The power of my cannocchiale [telescope] to show distant objects as clearly as if they were near should give us an inestimable advantage in any military action on land or sea. At sea, we shall be able to spot their flags two hours before they can see us; and when we have established the number and type of the enemy craft, we shall be able to decide whether to pursue and engage him in battle, or take flight. Similarly, on land it should be possible from elevated positions to observe the enemy camps and their fortifications.
So Galileo was already suggesting a possible use of telescopes at sea in 1609.
The letter is apparently quoted from Zdenek Kopal's Telescopes in Space (1968).
At the Battle of Copenhagen in 1801 when Admiral Nelson was signaled to retreat, he "turned a blind eye to it":
Nelson ordered that the signal be acknowledged, but not repeated. He turned to his flag captain, Thomas Foley, and said "You know, Foley, I only have one eye — I have the right to be blind sometimes," and then, holding his telescope to his blind eye, said "I really do not see the signal!"
Here is a list of naval battles that includes what seems like hundreds of battles between 1608 and 1800.
First hand accounts of those battles may mention captains and admirals using spy-glasses.
First hand reports of exploring expeditions in the 17th and 18th centuries may mention use of spyglasses.