This question is not irrelevant, but leads us deeply into Guru Yoga and realization of mahamudra. We are considering whether or not beings exist in subtle realms, whether or not liberation and enlightenment exist, and therefore whether or not Buddhas exist.
If Buddhas exist, it follows that liberation and enlightenment exist, it follows that beings exist in subtle realms, and because these phenomena are even being considered in this coarse realm, this indicates that people have experience and have shared about these subjects. There are many reasons we can use to establish the existence of these things, and by relying on this our faith, effort, and inner experience are empowered.
The very existence of the Dharma and its profound explanations clearly indicate that liberation and enlightenment exist because they are produced by causes, and these causes are enumerated in outrageous detail. In particular, the explanations in Highest Yoga Tantra explain very very precisely what the basis, path, and results are. When you read these, it is hard to think all this was just made up to deceive people in order to control them and extort money and servitude from them. Such descriptions are further supported by detailed explanations of the qualities of high bodhisattvas and Buddhas, and these are further supported by a plethora of remarkable anecdotes and the display of actions, miracle powers, and astonishingly precise clairvoyance.
People that disbelieve the existence of these things haven't experienced them in person, haven't read enough to make an informed and conclusive decision regarding their disbelief, are not really interested in spiritual matters, or are simply afraid of the implications. Sometimes, it even happens that people who previously had faith develop disbelief and proceed to try and come up with all sorts of reasons to disprove these things. Why? It is generally because realizing how challenging it is to complete the path, they want to feel ok abandoning the Dharma so they attack it in order to make themselves feel justified in following the path of least resistance: non-conscientiousness.
That's ok too, they're just not ready to follow the path to permanent liberation from suffering. Their time will come.
In waking life we can see that negative minds can reduce and positive minds increase. From this we can infer that by abandoning the causes of the former and refining the latter, we can develop powerful realizations that are clearly evident in anecdotes of Masters. Even in worldly activities, through familiarity we make less mistakes and perfect our 'outer' craft, so why should it be otherwise with the internal 'craft' of training the mind?
Furthermore, lucid dreaming and out of body (astral) experience are readily accessible to people either naturally or with a little effort. Those who do have experience and who apply techniques are able to refine their abilities in these subtle spaces. Lucid dreaming techniques, dream yogas, astral double training, the 9 mixings of completion stage of Highest Yoga Tantra (see book Clear Light of Bliss) - all these things show us that we ourselves have the qualities within us that through refinement can be brought to perfection. If subtle astral bodies and dream bodies exist, it follows that beings with subtle bodies such as spirits exist, and since there are elaborate Dharma methods for refining and perfecting these bodies and elaborate descriptions of the qualities of beings who have realized these things as well anecdotes of such beings showing clairvoyance, including Protector Oracles, it follows that Buddhas exist.
If we don't know if these things are real and yet having read or heard stories of people today who have this experience we still doubt, we are not being reasonable and should provide solid proof establishing the non-existence of all these things. Simply put, what it boils down to is that those with faith and effort experience the benefits, while lazy people who prefer to be skeptical and hold their ridiculous doubts firmly without even having valid reasons for doing so will not experience the benefits. Who in their right mind would not at least wish to be a person completely free from suffering, who experiences complete fulfillment, and helps everybody.
