Some of the very earliest did not, though a key reason why this was so was that the field attracted quite a lot of poorly educated autodidacts with a very limited understanding of the physics of water pressure.
A good example was John Day, a ship's carpenter whose early "submarine" - I used the word loosely, as the vessel was really nothing more than a reinforced chamber inside an adapted 50-tonne fishing boat, lacking any motive power – was lost when it was submerged to a depth of about 130 feet in Plymouth Sound in 1774.
Day had successfully conducted test dives at 30 feet and agreed to the experiment as part of a deal done with a gentleman gambler, one Christopher Blake, who funded the construction and in return took wagers on the likelihood that Day could survive underwater for 12 hours. He seems to have understood almost nothing about water pressure - the reinforced compartment he built was a cube, not the classical spherical shape favoured today, meaning there were corners where extra stress would be placed on the caulking – and he did not apparently realise that the pressure per square inch at his diving depth would exceed 72 pounds per square inch.
Bubbles of air probably produced by his chamber exceeding its crush depth were noticed soon after the ship was submerged and Day's body was never recovered.
A second known example of an early submarine being lost when it exceeded its crush depth was that of the – equally badly designed – Flach submarine lost in 150 feet of water in Valparaiso harbour during the Chilean guano conflict with Spain in 1866.
By way of contrast, by the time that Simon Lake began construction of his submarines in the 1890s, the danger of subjecting a boat to the stress of diving at significant depth was well understood – so much so that, unlike his rival John Holland, Lake refused to submerge his craft by diving while underway, and instead preferred to have them stop dead and claw themselves beneath the surface using small horizontally-mounted screws in order to better control the rate of their descent.
Robert Fulton noticed. When he tested his Nautilus off the coast of Brest in 1801, he and three others took it down to a depth of 25 feet and stayed there for an hour- but during the test Fulton decided it wouldn't stand the pressure of a greater depth. He would later consider some sort of a safety valve to be used in case the windows broke- but it was never tried, and his submarine project never fully matured. Though, it did meet Fulton's purpose of extracting money from the French, then the British.
Fulton got the idea for his submarine project from that of David Bushnell's Turtle, which was unsuccessfully used against British warships during the American Revolution, and little is known of Bushnell's thinking. It was intended to be employed at a shallow depth, however- gliding unseen below the surface of New York harbor, attaching an explosive charge to a British ship, then gliding away. It had windows at the very top and no periscope ( which came later in the mid 19th c.) so the operator couldn't see if deeply submerged. Fulton's illustrations show his submarine also at rather shallow depths.
Operating a submarine by human power ( which is what was available) severely limited what they could do. As a submarine has to displace the equivalent weight of water in order to sink, it needs to be a pretty heavy thing. That mass has momentum, and as Bushnell's pilot discovered that's an awkward thing. When he tried to make the Turtle sink, it kept sinking, when he tried to make it rise, it kept rising, and the British standing watch on their ships saw an object porpoising through the water towards them and were immediately suspicious . Fulton seems to have decided his submarine would sail on the surface to where it needed to go, and would then sink to a hidden depth and lie in wait. But he never actually developed it, taking his money from that venture and moving into building a steamboat.
Wallace S. Hutcheon, Jr: Robert Fulton: Pioneer of Undersea Warfare