"Plate tectonics" means something a bit more specific than "convection currents with the surface of the fluid freezing". In particular, it implies 1) relatively large stable plates, 2) organized regions where crust is created/destroyed, and 3) large horizontal movement of those plates relative to each other.
Prior to ~2 billion years ago, Earth didn't have plate tectonics. You had large vertical motion (not horizontal), and creation+destruction of crust, but no organized centers where this was occurring. In other words, you didn't have large plates and what plates there were did not move long distances horizontally.
As another example, Venus has tectonic activity (it's periodically resurfaced and has volcanoes), but it doesn't have plate tectonics. You see regions of compression and extension, but no subduction zones and spreading ridges.
It's likely that what we call plate tectonics requires abundant water, at least on "rocky" planets. Hydrous phases of silicate minerals are required for the very weak faults and localized weak mantle required to have subduction. Without subduction, you don't have plate tectonics.