@Austin Berlick, it is hard to give advice with the very little information you provided and your PROFILE absolutely tells me nothing about you. Please utilize it for your benefit and for us to get to know you.
My random thoughts on your question:
1. Since I don't know your age, Real Estate Goals (long range, not interested in your short range goals), Your Why, and your real estate experience it is hard for me to provide meaningful advice.
2. If I look at this from purely a math problem then here is how I see it. 450k purchase 30k down, Mortgage 420k, 30yr@ 6.5%, Taxes 9k/yr, Ins 1.5k/yr, HOA (New Built, $100/monthly) 1.2k/yr, PMI 2.1k/yr ($175/monthly); For a total monthly payment of $3800. Charge 3 roommates 1k per month (3k) and your out of pocket is $800 per month. As a math problem this works out as you say and in a vacuum you move out 12 months later and now get 4k monthly with 4 roommates this on paper works.
3. Theory and Reality is not likely. Your vacancy rate is going to be much higher than what I calculate for long term housing 5%. You will be the glue to make everything work well while you live there but when you move out who is going to be the sheriff to run the household? There are people doing what you suggest and it is possible but with little experience your failure rate is going to be high. Again I don't know anything about you and your experience to tell you if it is a good idea, so I will default to probably NOT!
Now may I suggest a possible alternative? It won't meet your 20min rule but if you can live for a couple years just outside Austin then your plan could work well! Let me explain not with theory but with real world example. Duplex buy in Elgin, double your time 40 mi to downtown with tolls. REAL WORLD, just closed on a duplex LAST WEEK! Price 270k. We will use your downpayment of 30k (owner occupant) same 30yr mortgage, PMI 100 monthly, No HOA and INS 1500 per year. Total Monthly Payment $2160. Duplex is 2 Bedrooms 2 Baths with one car garage each side. Rent out one side $1500 and your side, rent out a room for $700/monthly you're living Free. Your vacancy rate is far more manageable and when you move out your rent both sides for $1500 each for 3k/monthly and you're making $800 a month. Now full disclosure at time of buy one side empty, one side rented for $1050 Jan 2024 term. Each side identical. Signed lease yesterday with new tenant for $1500 no work needed on unit.....rent ready at buy!!!!. I will have to wait till Jan 2024 to raise rent to $1500 on the other side!!!! This was on the MLS. https://www.zillow.com/b/805-l... same pictures that was used to sell. We advertise for rent before we owned with permission of seller.
Live in this situation for a couple years, get some experience as a landlord/investor and then you are ready for whatever the next step is. Your success rate will BE MUCH HIGHER than the plan you worked out. Again I don't know what your long term goals are, this might not be great short term but long term it is a HOME RUN. I care not what the short term goal is if it is a detriment to the long term goal. Again I'm an old fart 67 prior fighter pilot and I don't care much about feelings and more about accomplishing the mission. Sacrifice now and live like a King later. Live like a KING now and maybe struggle the rest of your live. Right or wrong I will shoot you straight. Good Luck.