A: We all do what we have to do - training time, coaching, and space might not be something we can dictate, so if you have to train first thing in the morning, then that's what you have to do. But, the lower back is at greater risk of injury from load bearing activities immediately after waking. Most people are aware that the spine relaxes and the spinal discs absorb fluid and lengthen while sleeping. It is not uncommon to be a full inch taller in the morning.
So what? So, in "squat-speak", if you are normally a high-bar squatter, you'll be essentially doing a Manta-Ray squat first thing in the morning. If you are a low-bar squatter, your lower back is doing high-bar squats when you first wake up, whether you like it or not.
Does this mean you can't squat or train intensely in the morning? No, but if possible you should wake a little earlier to give yourself time to properly warm-up for your training.
Q: What should I do differently to warm-up if I decide to squat in the morning?
A: In my opinion, taking extra time to do some extra stretches and mobility work, and extra lower intensity warm-up sets preceding the main work sets would be a good place to start. Form is always paramount, but in the morning the body may be even less patient with small errors and inconsistencies - make sure that you are attentive.