With your salary, you should be able to accomplish something. However, it is important to note whether the price you mentioned stays the same or if the offer is one of those deceptive packages. How about incidental building costs, are they already included? What else is missing from the offer? Usually, only the pure construction costs are mentioned, but not the incidental building costs.
If I were in your position, I would tighten my belt now and save strictly for 2 years. With your rent, there is easily €2,000 monthly available. If not, financing will become tighter as well. As already mentioned, you should expect a monthly rate of about €1,500-2,000 if you want to finance €300,000. Then the house will belong to you after 20-25 years. Additionally, you have to calculate €300 for incidental costs for the house, which already includes reserves.
Especially if children are not an issue anyway, you have various freedoms and can also build a bit smaller. After all, you want to have it all cleaned :)