With the "quick add" task entry tool, you can create a new project just by typing the # symbol, and then writing the project name. The only catch is that you can't use spaces, but that's something you can easily live with if you want speed.
E.g. If I've identified a next action "check under stairs for tape measure" as part of the project "install bigger fridge", then I would type it into the todoist quick-add box thus:
check under stairs for tape measure #install-bigger-fridge
This allows you to create the project on the fly, without even needing to click anything.
If you're using labels for contexts, then you're really off to the races, because you can also type them:
check under stairs for tape measure #install-bigger-fridge @home