The former Arizona Cardinals quarterback signed for the AFC East side earlier this month.
The 28-year-old told reporters: "I am here to win a Super Bowl. Period. There are very limited opportunities in this league. I have been lucky enough to have a few of them.
"Hopefully have another one here and plan on taking 100% care of that and making sure I do my part to play at the highest level.
"For me, I know I can play at this level. I have done it here and there throughout my career two or three games at a time."
Kolb previously played for the Philadelphia Eagles, before joining the Cardinals in 2011.