When a master cylinder fails, the pedal will sink to the floor when holding steady pressur on it. Early signs of failure are that it sinks slowly. Advanced cases the pedal sinks more rapidly.
It doesn't sound like what you are experiencing.
It sounds like you are feeling the change in load on the powertrain as the slack is taken up from engaging the transmission. It is more noticable when cold because the engine is idling faster and the trans fluid has not warmed up yet. It is probably a normal condition, but I can't really tell from long distance. If you are still concerned, have an expert start it cold for you and get their opinion.
