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 Prices in Urban Area

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.
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.
Land Appreciation Example

This 3.2 acres undeveloped land was appraised by Harris County $25k in 2017 and 2018, in 2023 and 2024 appraised $279k. Land value increases as population increases, more people looking for housing and more land needed to build housing. Raw land, or undeveloped land, do not have road or utilities ready, and price is lower as an additional cost will be needed to get it ready. Developed land has road and utilities ready, typically market priced starting $50k per lot.
Land Appreciation Example with Development and Size Factors

This subdivision has a typical lot size of about 6000 ft2 in a less developed area of the city of Houston. In 2024, a developed lot, with public road frontage and utilities, each lot was appaised by Harris County Appraisal District to have market value of $55k. For lots that do not have road frontage, where the roads are only on paper but trees not cleared and road not built, and utilities a few hundred feet away, were appraised to have an adjustment factor of 0.5, so that market value of each lot was $27.5k. Some of the lots were divided into two so that each divided lot is about 3000 ft2, then the Appraisal District assigns a size factor of 1.5 so that market value is the undivided lot value divided by 2 (half area) then multiplied by 1.5 (size factor) to result in $41.3k.
Land Appreciation Away from Cities

In rural area away from cities, land value is mostly based on agriculture yield.
As this
chart
shows that soybean yield per acre has been increasing, land value per acre will also be increasing above inflation.
Raw land far from the city could have prices like $0.1/ft2 with sufficient rain for farming, or as low as $0.01/ft2 for large sized desert land.
To build homes on rural land, water and wastewater treatment would be additional cost. If allowed, lowest cost would be composting toilet. If composting toilet not allowed, septic system could be low cost but typically about 1 acre land is required per home. For higher density, wastewater treatment plant would be required, but cost per home could be low with hundreds homes or more.