You get used to eating close to a workout or drinking a shake pre workout. It's something I was never able to do. I remember not long after I started, seeing this big guy eat fruit during the workout, and I was amazed he could train with it lying in his stomach.
Since I started working in my gym I need to take my calories when I can. Sometimes I knock back 50g carbs, 50g protein, in about 2 minutes, then go warm up and train (and drink a shake during the workout). I'll often go to the supermarket across from the gym, buy cooked chicken, eat till i'm full, then warm up and train. I wouldn't recommend this, but if you do 6 back to back appointments, at the very most, all you'll manage is a quick shake and you get kind of desperate for solid food. Then your "window" for solid food and training time is the same, so you need to eat close to it. At first it didn't feel good but now, I have no issue working out quite soon after eating. I think it helps that the first portion of my training days are more strength related so, there's not really much "getting out of breath" involvd. Mostly just straining. If I was doing intervals or complexes or something at the start, there's no way I could eat so close to it.