Use savings to buy land
If you can find a lower priced smaller home (starter home) that you can afford, you can go directly to buying a home. This includes pooling funds to buy an apartment building and converting it to a condo. Otherwise start buying land to build starter home. Land opportunities include land with building(s) on it with room to add building.
Land price is typically higher closer to a city center. It is also higher in areas with better schools, more amenities, and lower crime rates.
If land is not ready to build on, such as lacking roads, water, sewage connections, etc. Price is lower as an additional cost will be needed to get it ready. Raw land far from the city could have lower prices, like $0.1/ft2, or $0.01/ft2 for large sized desert land.
The city of Houston allows 1600 ft2 lot for a single family home, and no limit for courtyard style.
Since a duplex can be treated as a single family home, owning one unit of a duplex in 1600 ft2 land means owning 800 ft2 land. If land price is $20/ft2, that 800 ft2 would cost $16k.
It is more difficult to get a loan to buy land, especially when you are young. Consider borrowing money from family members if you've saved up 20% for a land purchase.
Alternatively, you can put savings into a land fund to buy a share in land until you save up enough to buy your own parcel of land.
Land ownership may be used to replace down payment when building home. If you decide to move, you can sell the land (and the home if built), likely at higher price (use 1031 or similar to avoid paying capital gain tax), and buy another parcel of land or home.
Examples of American Teenagers buying homes