When first starting out the car hesitates then accelerates normally after about forty seconds

Just to be sure what the issue is. The car starts fine but when you first put it in gear it doesn't want to accelerate but the RPM goes up like normal. The vehicle just doesn't move very fast? All most like it is bogging down? Does it sound normal when you are accelerating or does it not sound right either?

I am thinking we either have a sensor issue like a MAP or throttle position but we should have some codes with that so let's start with checking the codes.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Then we need to check the basics like a vacuum leak and fuel pressure.

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

It may be a leak when the engine is cold and then the gasket warms up and seals itself.

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

I don't think it is a fuel issue just because it is working properly a short time later. However, we need to cross it off the list or we will be chasing our tail.

Let me know what you find with this and we can go from there.