Recently I learned a new term: garage shift. It's what a cold transmission will do when it's first being asked to do anything, like being driven out of a garage. Anyhow. My two thoughts: first, check fluid level. Cold fluid is at its least "large" size, as it shrinks with temperature. Maybe you just have low fluid level. Second, maybe there is an o-ring that needs to warm up a bit, or it is taking a while for the system to pump up. Maybe the pump is on the way out.
Not that it's really relevant, but my old '99 Camry, if I didn't let it idle for about 20 seconds on a cold start, it would go into reverse just fine. But go into drive? it was in some gear between 1st and 2nd. I put over 50k on it, and really, if I just let it idle for 30 seconds before going anyplace, it wasn't noticed. This isn't the same car, so I'd have it looked into.
How many miles on it? If it's overdue for a change then it's a pretty good sign that it's overdue.