I'm sure a lot of others will have a similar answer here but just want to address your concerns.
You don't need to know anything about property management, you can outsource that to a property management company.
Finding good deals just takes time. The first thing you'd need to do is set your criteria on what a "good deal" would look like to you.
The logistics of owning at a distance are first and foremost to build a trustworthy team. @David Greene (I think) coined the term the "Core 4". You need a trustworthy and competent real estate agent, property management team, contractor and lender. Investing long distance is all about leverage and building trust.
Now your last point, why real estate instead of VTSAX (had to Google that) is an index fund gives you appreciation long-term, but not much else. With real estate, you generally should see appreciation long-term, cashflow each month, tax benefits that can lower your total taxable income, equity growth as your property is paid down by your tenants over time, plus you can add value to the property by making improvements.
With an index fund, you really are at the mercy of the market and have no control over how that investment performs, like you do with real estate.
If you were really interested in real estate, you could check out the podcast and some of the books BP published like The Book on Long Distance Real Estate Investing, especially since you live in Brooklyn.