When is the soonest I can get my baby into a routine?

Sooner than thought. Day 1 is not too early to start. You can help shape your newborn's behavior by working on a consistent eat/play/sleep pattern by day and eat/sleep by night, starting when you get home. Most babies can be on a consistent three-ish hour routine/schedule by 2 weeks of age. Two caveats: 1) baby cannot be held 24/7 and 2) you will need to tolerate some fussing at times. Discuss with your doctor.
After 3 months. After 3 months of age, most babies can stay with a routine. Before then, one should not try too hard to establish a routine. However, it is ok to let 1-2 month old babies sleep through the night if they are healthy and growing well. After 3 months of age, most babies can sleep a 5-6 hour stretch at night.
8 weeks. 8 weeks is still pretty early, but it is around this time that babies will begin to consolidate daytime sleep and sleep for a bit longer stretches at night. A morning nap will appear first, usually around 9am. Try putting baby down at this time a couple days and see if they are ready for a nap. A mid-day and afternoon nap appear a few weeks later. Use consistent routines before naps.