Audible turntable rumble is exaggerated by the RIAA equalisation necessary to playback vinyl.
You can reduce the amount of rumble with a well set-up turntable, but it’s impossible to eliminate it altogether, and the equalisation amplifies it.
It’s one of the ways in which vinyl is a flawed system, and most of the time turntables’ expense is down to trying to negate the flaws as much as possible
Rumble is inherent to any mechanical rotation and thus not totally avoidable, indeed.
We should probably clearly distinguish between audible rumble and subsonic rumble. The latter is not as much of a problem as some might think, as it can be rather easily dealt with. IEC came up with modified RIAA EQ (including subsonic filtering) ages ago. Matching of cartridge compliance and effective tonearm mass is much more complicated than applying the well known (and completely inappropriate) formula for an undamped spring-mass-system on one hand. But it's also far less critical, because there actually is damping and polymer cantilever bearings don't have one fixed spring-constant.
Rumble in the audible range could be reduced by higher crossover frequency rumble filters, but by very nature these affect the wanted signal just as much as. If there really is such wanted signal, at all. Many LPs are mastered with little or no audible content below ~40 Hz (easy to check e.g. using Audacity). I have to agree with
@cooky560, that very often audible rumble is really caused by bad pressings or bad mastering, but if it's on the physical media, then eve the mechanically most perfect turntable cannot improve the situation.
However, I'm pretty sure that
@bgaldo's problem is not related rumble, nor wow, nor flutter.
I would check cables and output voltage settings.