Alternatives of financing such as rent-to-own, etc.

Just inquire at a Turkish bank

Then everything is Halal

Hire purchase or partial sale is an absolute exception despite all the advertising. There was or perhaps still is the purchase of housing entitlements in Austria. One buys a right to reside but does not acquire ownership.

How about an inquiry at the Islamic KT Bank? They advertise with Sharia-compliant financing models.

Otherwise, borrow money from friends and family?
Otherwise, the only option left is to seek advice in the community or mosque on how other believers have solved this.

Are there actually options for house building companies or similar to build houses and offer them to me in the form of reduced rent and/or rent-to-own?

No. This is already "prohibited" by the fact that the landowner will be the owner of the house built on it. So if I, as an entrepreneur, wanted to build a house on your land, I would not find a bank to pre-finance it for me, since the house would not belong to me but to you. I see the opposition to capitalism as controversial regarding the topic of property ownership or acquisition. That does not fit. There is a major misunderstanding.

I see the opposition to capitalism as controversial regarding the topic of property ownership or acquisition. That doesn’t fit. There is a big conceptual error there.

Criticism of interest is not the same as criticism of capitalism. Bazaars in Islamic countries are capitalist hotspots. If you set religious, ethical, moral, or other framework conditions for yourself, that’s okay. If you don’t like interest, you can find a bank that adds up all normally due interest for a full repayment loan and lists it as a closing fee. Then the total sum is repaid over term X and nowhere does the word interest have to appear. Things like partial repayments and corresponding interest savings could be renamed as discounts or bonus payments. As I said, there is a German bank that can finance real estate according to Islamic principles. It would be very interesting to learn how that works with banking supervision and other legal regulations. This all reminds me of the euphemism “savings plan with immediate payout.”

If you don’t like interest, you can find a bank that adds up all the normally due interest for a full repayment loan and shows it as a closing fee. Then the total amount is repaid over term X and the word interest doesn’t have to appear anywhere.
Something like special repayments and the corresponding interest savings could be renamed as discounts or bonus payments.

It’s not about dodging the word interest to lure someone who has a problem with interest. It’s more about the attitude “I don’t like paying interest.”

And Islam could also be put in brackets once.
I don’t see anything from the original poster that indicates otherwise.