Could a dwarf galaxy host a star at the center instead of a SMBH? I don't think this would be possible, but I'm curious, and as what ever query I googled I only found posts about black holes indeed existing, what black holes are, that even the Milky Way has a black hole in its center or that We can't know if dwarf galaxies have non-SMBH at their center.

So sorry if it is a stupid question but I didn't want to go on with assuming something without knowing: So is it theoretically possible for a Galaxy to have a star at its gravitational center of mass?
A galaxy's center of gravity is not determined by the most massive object, but by all objects in the galaxy. Even supermassive black holes (SMBHs) do not dominate the gravitational field except very, very close to the center. By far, most of the stars in a galaxy couldn't care less about the SMBH.

The region within which a BH dominates over that of the stars (the "sphere of influence"$^\dagger$) is given by (e.g. Peebles 1972)
$$
r = \frac{G M_\mathrm{BH}}{\sigma^2},
$$
where $G$ is the gravitational constant, $M_\mathrm{BH}$ is the mass of the black hole, and $\sigma$ is the velocity dispersion.

In the Milky Way (MW), there's a SMBH (Sagittarius A*) of roughly $M_\mathrm{BH} \simeq 4\times10^6\,M_\odot$. In that region, the stellar velocity dispersion is roughly $50$–$100\,\mathrm{km}\,\mathrm{s}^{-1}$ (e.g. Genzel et al. 2010). Plugging in those values, you'll find that Sgr A* dominates the kinematic out to roughly 3 pc, or 10 lightyears, which is nothing compared to MW's radius of $\sim10^5$ lightyears.

If you take the most massive conceivable stars (a hypothesized Pop III star of $M\sim10^3\,M_\odot$) in Willman 1, the smallest known dwarf galaxy — which has stellar velocity dispersion of the order $5$–$10\,\mathrm{km}\,\mathrm{s}^{-1}$ — you'll find that such a star will dominate the gravitational potential out to a distance of only $\lesssim0.1\,\mathrm{pc}$, again completely negligible compared to the galaxy's radius of $\sim25\,\mathrm{pc}$.

In other words, although it's possible for a dwarf galaxy to host a massive star, it will just be a star like all the others, and will in no way define the galaxy's gravitational center.



$^\dagger$Not to be confused with the event horizon which is even smaller.