Just a minor nit: SentencePiece is a library, not a tokenization algorithm. It implements two tokenization algorithms, Unigram and BPE.

BPE builds vocabularies from the base up so I assume you are talking about Unigram which starts with a big vocabulary and trims it.

The details of UnigramLM are here https://arxiv.org/pdf/1804.10959, and the part about vocabulary seeding is Section 3.2.

Basically, it just selects all substrings that appear in the corpus up to a certain length (and then maybe trims it a little by discarding rare substrings or something to reduce the initial size a bit and make things faster).