You need just enough money to conduct business. Gas money/car expenses, cell phone bill, and some legal paperwork. I think right now in 2024, if you're working a full time job OR you have $3,000 saved up, you have enough to start. It's not the ideal way, but it's doable. I started a real estate business with $5k in savings last year, and I didn't use all of it (keep in mind that I had business experience).
But... you've got to hustle like crazy. Use some of the money to go find private money investors. Build relationships. Go to where they are. Buy drinks, coffee, lunch and make some friends with money. Network. Find some private money where you can bring the deal and do the work, and your partner can bring the capital.
Then you don't need to worry about saving up to buy a rental. Study the BRRRR method of investing (David Greene's book is great). And watch Austin Rutherford on YouTube. No money down. But yes, most of the gurus won't tell you that you do need just a little scratch to do the hustling and get those relationships, file LLC paperwork, etc. Great job saving up $1k! Keep working, keep saving, and go do it. You don't need much. You got this!