On a brand new shamisen, that neck fitting should be incredibly tight, but it should fit. The maker will have undoubtedly put it together before taking it apart and shipping it. If you leave it as is it will eventually work its way in, but the fitting will be looser than optimal.
One of the drawbacks of not having a teacher is that you don’t have someone to show you this sort of thing. With my first new shamisen I also thought that there was something wrong with the neck fitting, but my teacher showed me how to take it apart and put it back together, and assured me that it was supposed to be a very tight fit.
To close that little gap you have, stand the shamisen on your lap (sitting seiza style on the floor is best, but sitting in a chair with your legs together will also work) so that the nakagosaki, the end of the neck sticking out the bottom of the body that the neo string holder fits on to, is in the space between your legs. Grab the neck just above the dou (body) and pull it sharply down in to the body. You might need to do it a few times to get the force right (you’ll underestimate how much force it takes), but when you get it right, it will audibly click into place.
Taking it apart is a similar process involving a sharp knock to the dou with the heel of your hand. A video of this might be better than a written explanation.
All neck fittings eventually get loose from years of taking them apart and putting them back together, but there’s no good reason to rush that process along. Making sure the neck is all the way in will also allow you to properly tie the doukake arm guard onto the body - the strings should not be in that gap, as it will cause the fitting to get looser faster.