Although you would ideally start shmonei esre at netz hachama, you can pray shaharit from misheyakir including talit and tfilin. In your case, you can start your tfila from 6:02 (see e.g., here at chabad under misheyakir or Halachipedia)
What would be more tricky is if misheyakir would be at say 6:20 and you had to leave at 6:45. In this case you can say all prayers until yishtabach without talit/tfilin, wait for misheyakir, put them on at that time then continue. See here on MY.
If you cannot put on talit and tfilin in the morning, you can do so later until sunset (see here), beyond that see here.
Very nice summary by R Eliezer Melamed here.
As always, ask your rav before applying anything you read here.