If you can't get a (high) fuel pressure gauge on it, you might try the following for first start in the morning. (if the problem persists after you change the filter, that is)
Key off > key on ; you should hear the pump run for a short time. Keep repeating this several times, adjusting the key off time to make sure that the short priming cycle is done on the fuel pump each time.
If it runs OK on first start after this, it is most likely that the fuel pump is "leaky". That is to say that the tolerances between the vanes or roller are such that a significant amount of back flow happens when you are stopped, and that fuel delivery is reduced when it is running - but it can be something that won't be noticeable once you are going.
Hope this will be of some help to you.