ございますれば is a double punch of archaic speech. First, polite ます's 仮定形, ますれば is effectively obsolete, as we don't insert a polite marker in a clause led by れば. When a politer conditional is needed, we use ましたら instead. Second, the れば is not "if" but a remnant of old 已然形 sense "since, because". The dictionary says:
This reading is only valid today in few idiomatic phrases, namely なれば (=であるので, なので) and ますれば (=ますので), both sound fairly quaint. Otherwise this kind of expression would never be used lest be confused with normal 仮定形 sense.
As for the interpretation of this sentence, その人唯一の存在 is a little problematic. Under this context, it is most naturally understood as "the unique existence of oneself", but the
N唯一 formula in principle should tell "only one that N has": 東京唯一の支店 "the only branch in Tokyo", 彼唯一のアルバム "his only album". In this light, the sentence may also be able to be read "because a person is always the only one for someone".