Mini house - possible for 300K €?

Have a listen around your area. Carpentry in town for new construction, stone on stone the little mason. I would continue to look at the existing stock

Yes, carpentry is also a good idea, there are indeed well-made wooden houses.

I came across an article in the FAZ about such a project. The mentioned single-family house was built in 2014 in the Münsterland region using a timber frame construction, has 115 sqm of living space, and is said to have cost approximately 162 thousand euros gross. So it is basically possible, but it was built with interested architects. Keywords for the search are "FAZ Haus Sozialarbeiter".

It's common among Americans...

Just today in the San Francisco newspaper. The move only costs €330k.

In America, everything is just a bit bigger, including the trailers. The Dutch really can't compete.
There are those tiny house concepts on trailers that you can tow with a 7-ton truck. My girlfriend would buy one immediately, but I’m not moving out of the 65 sqm apartment just to live in 55 sqm with the three of us ;)

Everything that has wheels is and remains a caravan. The trendy thing called Tiny House doesn't change that. Sure, it all looks a bit snazzier, more modern, and cuter, but it remains at caravan quality. Do you know what also looks snazzy, modern, and cute? Garden houses! For example, the log house Lukas-94. 70m², under 90,000€.

About the project itself... I assume 87 is the birth year and you are the same age as me? For such a tiny house, life planning must not change much anymore.

The answer to the question of whether an extension is theoretically possible should at least be taken into account in the purchase decision, that's true. If not, I would at least choose the house so that in case of a changed life plan it still serves as a tolerable transitional solution. With the new partner, the pubescent offspring and the dog on 70 m² - the joy of moving in together won't last four weeks. I recommend the OP to keep an eye on the urban terraced housing estates first. That would definitely fit better with the mentioned budget.