Does a dvt happen gradually or suddenly?

Symptoms are gradual: A deep vein thrombosis happens usually suddenly but the leg pain and swelling that lead to the diagnosis tend to evolve over some hours. The larger the thrombus is the more quickly the symptoms become severe.

A little of both: The beginning of clot formation is probably fairly sudden. Growth of the clot is more gradual. Initially, when the clot is small, the pain and swelling it causes is less severe and is more likely due to the inflammation that the clot produces. Once the clot is big enough to completely block a vein (especially a large one) the increase in pain and swelling can be sudden and severe.