Can a submarine go to the bottom of the sea?

Define "submarine" and "bottom of the sea".

Submarines are designed for a particular pressure/depth. The designers also incorporate a margin of error, so the actual depth at which the submarine would be crushed by external pressure ("crush depth") is generally marginally greater than its "design depth". Submarines normally operate at a fraction of their design depth (this is called "test depth") under normal peacetime conditions. Different navies use different fractions as the test depth; the German navy specifies a test depth of half the design depth, while the US navy uses 2/3 of design depth.

If the sea floor depth at a particular point is less than the sub's test depth, then they can approach it (though, for various reasons, actually touching it is nearly always a bad idea).

The deepest known point in the ocean is the Challenger Deep in the Marianas Trench, at about 10,916 meters. Two human-manned vessels (one solo craft and one with two occupants) have gotten within a few meters of the bottom there, but both of them were technically "submersibles" rather than "submarines"; they had limited mobility and basically existed to go primarily straight down (and, hopefully, back up) rather than cruise for long distances horizontally. Actual submarines generally have much lower design depths. For example Virginia-class US nuclear attack submarines have a test depth of only about 240 meters (putting their design depth at about 360 meters).