Is it possible to create a point within a Polygon (not a centroid)?

If you do not care about whether the point is a centroid or not, just use Vector -> ResearchTools -> Random Points. You may define to place a single point per each polygon in a layer. Also you may create centroids for initial polygons, delete points that do not intersect any polygon, save polygons without points as a separate layer, create random points for this polygosns and in the end copy these random points to centroids layer.

EDIT : answer by @Kampau Ocu : "point on surface is already within QGIS3 Processing Toolbox"

You can also use the plugin RealCentroid that does just what you're looking for :

RealCentroids plugin creates a point shape file with internal points of a polygon shape, similar to PostGIS (GEOS) ST_PointOnSurface. The point will be inside the polygon in all cases. Not only the points are created but the attributes are also copied from the polygon to the internal points . A single point is generated for multipart geometry too.