2001 Sienna with intermittent starting problems

I have this van that turns over to start but just won’t start. It’s an intermittent problem, and NEVER happens when the mechanics try to diagnose it. It does eventually start if I keep my foot on the gas, but once I take my foot off the gas it dies. It doesn’t even think about idling- it just stalls out. Once the engine warms up it’ll stay running, but I’m afraid it’s only going to get worse. I’ve had it in twice for the same problem, and their computer shows no failing systems. It seems to happen more in the cold, but sometimes it starts fine when it’s cold, too. We’ve replaced the battery, but that was not the culprit. Any help would be greatly appreciated. Thanks

All cars sold in America have an 8 year, 80000 mile warranty on the catalytic converter and all the devices and sensors associated with the emissions control systems. It’s possible you are still covered; you did not say your mileage. This problem might be covered.