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The ending of becoming (bhavanirodha) is exactly the goal of Buddhism.

>'When a noble disciple has thus understood being, the origin of being, the cessation of being, and the way leading to the cessation of being…he here and now makes an end of suffering. In that way too a noble disciple is one of right view…and has arrived at this true Dhamma.'
(MN 9.31 (p 137))

The cessation of becoming should not be confused with non-existence (vibhava), that is, the belief that an existing self becomes non-existent (see Iti 49), still, that is called the best outsider view (AN 10.29). What bhavanirodha means is nirvana in this life (AN 10.7), and even if one has doubts one should choose that as the right view:

>'Now as to the recluses and brahmins who hold the doctrine and view “there definitely is no cessation of being,” if their word is true then it is certainly still possible that I might reappear [after death] among the gods of the immaterial realms who consist of perception. But as to the recluses and brahmins who hold the doctrine and view “there definitely is a cessation of being,” if their word is true then it is possible that I might here and now attain final Nibbāna. The view of those good recluses and brahmins who hold the doctrine and view “there definitely is no cessation of being” is close to lust, close to bondage, close to delighting, close to holding, close to clinging; but the view of those good recluses and brahmins who hold the doctrine and view “there definitely is cessation of being” is close to non-lust, close to non-bondage, close to nondelighting, close to non-holding, close to non-clinging.’ After reflecting thus, he practises the way to disenchantment with being, to the fading away and cessation of being.'
(MN 60.34 (p 517))

What should be recognised is that a being (satta) exists as craving and clinging (SN 23.2), and becoming is about deluded identification that is an outflow/defilement (āsava).