Sometimes you have to split an infinitive but not here: "and just to be" would be better, and perhaps easier to understand. "To be" = "to exist." "just" = "merely, only, nothing else." So "just to be" = do nothing except exist; relax, don't expend a lot of physical or psychic energy.
It's an entirely different topic but "splitting an infinitive" is inserting an adverb or adverbial phrase between the particle "to" and the verb itself. The infinitive form of the verb here is to be. Inserting the adverb "just" gives us to just be. The full infinitive has been "split" = divided into two pieces. There are probably threads about this, debating whether you may split an infinitive whenever you please, only when it is necessary, or never.