The capital letter indicates that ‘Spring’ is being used in the sense “the season between winter and summer”.
How can something be both “as young as Spring” and “as ancient as Spring”? This is a paradox, and to resolve it we have to think of Spring in two different ways. Spring is “young” because it is the first season of the calendar year, and because it the season when many animals have their young. (This is an example of metonymy.) But Spring is also “ancient” because Spring has been a season of the year as long as the Earth and Sun have existed, which in the mythology of Middle-earth is about seven thousand years.
If the voice is both young and ancient, then perhaps (by metonymy) so is the speaker: these similes are giving us a hint about the nature of Goldberry.
The word ‘spring’ has another meaning, “a flow of water emerging naturally out of the ground”. This is so close in meaning to the following phrase, “glad water flowing down … from … the hills” that it cannot be a coincidence, and seems to be a clue that Goldberry is (or resembles) a naiad, “a nymph of fresh water, thought to inhabit a river, spring, etc., as its tutelary spirit” (OED). Other clues to this are Tom’s description of her as “River-woman’s daughter” and her own description of herself as “River-daughter”.