Ok, it seems I have been wrong about this as a general statement and liberal (or even most?) jew movements indeed consider it possible.

Last time I checked - it seems I read a viewpoint from a rather orthodox rabbi (but his article was the first one, that showed up in google at that time, now I cannot find it anymore), which clearly stated, this is not possible at all, with no exception.

The only way, would be to recognized as a "lost jew", meaning being of jewish origin, who lost connection to the tribe (even some generations ago). And the recognition would need years of devotion.