The biggest hurdle to starting your own business while working is time management, as you stated.
As someone who has and is still currently doing this, you need to figure out how much time you have to work on your business, how much time you need to rest, and go from there. Trying to cram in everything will just get you burnt out, then you'll suffer at you own business as well as work.
First off, let me state that this is a marathon, not a sprint. Don't get ahead of yourself. That will likely only make you waste time when things make you change your decisions that your "thinking ahead" was based off of. Do things in as much of a logical order as possible and you'll actually save time and money, most of the time. If something is going to take a lot of time waiting for a 3rd party, like a government agency approving a permit to operate or whatever, make the steps to that a priority so you can work on other things while you wait for that task to complete itself.
Once you figure out how much time you have to invest, try to ballpark how much work you'll need to set up the business. Now double that estimate (at least), since it'll be way low. You likely don't know all the things that are going to delay you until they happen, so give yourself plenty of time.
Take breaks as needed, but don't waste time, either.
Next, set a goal for when your business starts operating as a business. This is not a deadline, just a goal. Goals can move around, deadlines generally can't. Your goals need to include who is doing what, since you have a partner. Some give and take can happen while working on the business, but you should generally know who is responsible for getting things done. This is not for blaming anyone if/when something doesn't get done, it's just so there is a more clear path forward since you know who is doing it and you aren't duplicating effort.
Once you get near your deadline (1-2 months out), revise your list of things that need to be done "now", as in before your business starts operating. If you can't make your goal, figure out what can be done later and if you need to revise your goal.
Once you have reached your goal, start doing the things. Don't bother with a "grand opening", as that wastes time, money, and effort that could be better used for your actual business at hand. A grand opening works only if you are a "brick and mortar" store and have a great location, anyway.
Once you start, make time to continue working on your business, not just fulfilling orders, creating/researching new products, etc. This is an absolute must. If you aren't spending time on your business, doing your business isn't going to really get you anywhere. You might get some orders, but not enough to get you away from the day job permanently.
Through all of this, be sure to get enough sleep and do stress relieving things. It doesn't help you to be stressed out, exhausted, uninterested, brain burnt, and unmotivated. It also doesn't help if you get fired from your day job if that's how you're paying to "keep the lights on" for your own business.
Also, be willing to listen to your customers. The customer isn't always right, but sometimes they are and sometimes they have good suggestions. Figure out which are the good and bad suggestions by asking your other customers. If a large majority of customers like the idea, think about implementing it. Make a plan for it first, then decide if it's really worth the effort.
BTW, your business plan is likely junk and full of guesswork. Go with a business model canvas instead. This is a one page "bare metal" details view of what you are doing and what you're going to do. If your business plan doesn't answer all these questions, you've unfortunately wasted your time, as so many others (including myself) have. Business plans are for medium to large businesses that don't plan on changing anything major anytime in the next decade, or so. They are a great thing to collect dust and have as a reminder of your naive/historical self from when you wrote it, but it doesn't really mean anything for a small company past opening the doors.
If you master all this, you might just be able to earn enough money to ditch the day job and go full time on your own enterprise. Not many can. I still can't, mostly because I haven't spent the time working on the business instead of the products. Also, don't ditch the day job until you can completely run your business without putting your own money in, as well as being able to replace your salary completely with the money you make from the business. You can "squeak by" with just covering your own bills, but that's not healthy as well as being a fine line between needing that job again and failing at your business.
Edit: With the business model canvas, the hardest section is likely to be the Value Proposition. This is what draws people to you on a "no question" basis. This is not a list of features or services you provide.
If you were a dog grooming company, your value props are not:
Trimming hair and toenails.
We sterilize our equipment between use.
Your value props are:
We understand your pets are your family.
We will pamper your pets as if they were our family.
We make sure to protect your pets health.
This is the part of Why people will come to You and only You. Literally anyone can wash a dog or import things from China, but why will they want to do business with you, rather than eBay or some kid down the street?
Got it? Probably not yet, but give it a few times and lots of consideration and you'll figure it out.