Q: My 2003 Toyota Sequoia starts then dies and does this a couple of times until it stays running. It only does this when it's cold.

Although it is a little cumbersome, you could try to rule in or out a fault in the fuel delivery system by having an assistant quickly introduce "starter fluid" into the intake right at the point (very quickly, of course) that the engine starts to cut out. Of course, you will do this experiment on a cold day. If the introduction of starter fluid keeps the engine running, during these stumbles, that would point toward a fuel delivery issue although the delivery problem could itself be the result of a faulty engine temperature sensor.

A faulty temperature sensor will mis-report to the PCM and not enrich the mixture at cold start-up thus causing the engine to immediately stumble. It is also possible that the relay that drives the fuel pump is cutting out during initial start-up. There are other obvious possibilities include the idle air control valve.

A certified professional, like one from YourMechanic, could perform an appropriate engine management diagnostic and get this resolved for you. By the way, to make your life easier, and assist you toward resolving this, the shop should have given you a detailed list of each and every component, system, or possibility that they already tested, so that you don’t have to re-invent the wheel.

I’m sorry to say that if they simply told you "they couldn’t find anything," and at the same time did not give you a reasonable level of diagnostic detail, they probably did essentially nothing to help you. Put another way, the symptom you are reporting is not of space shuttle complexity and thus it should have been fully resolved during your first visit.