My first day commuting by bike:
1. Followed bike paths on busy streets instead of sidestreets with little or no traffic.
2. Got a flat.
3. No spare tube, tire irons, pump, or patch kit.
My next day commuting by bike:
1. Followed a route with minimal traffic.
2. No flats, but was prepared if I got any.
3. Got to work and thought "Now why the HELL didn't I start this a long time ago!?!"
That was right about 30 years ago.
The only issue I would have is your ride home in all the traffic. Are there no alternative routes? Forget about speed ... it's about safety.
Edit to add: Don't worry about being exhausted on the way home, or exhausted when you get to work. More sooner than later, you'll find it exhilarating.
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Proud parent of a happy inner child ...