Learn Spanish (Latin America): Ya que son fotogénicos, se invita a los chicos a posar. - Since they are photogenic, the boys are invited to pose.

This is the impersonal se construction. Because the sentence uses the personal a before a specific human object (a los chicos), the verb must remain in the third-person singular. If you dropped the a and said se invitan los chicos, it would become a passive or reciprocal se, which could mistakenly mean 'the boys invite each other.' Using the personal a with a singular verb clearly limits the meaning to 'someone invites the boys' or 'the boys are invited'.

Could we replace a los chicos with a pronoun in this impersonal sentence?

Yes. If you replace a los chicos with a pronoun, strict grammar rules call for the direct object pronoun los, making it se los invita a posar. However, in many parts of the Spanish-speaking world, you will commonly hear the indirect pronoun les used here instead (se les invita a posar). This is a widely accepted practice for impersonal se structures involving human objects.

Is ya que the only way to translate 'since' here?

Ya que is very common for introducing a cause or justification, similar to 'seeing as' or 'since' in English. You could also use como or dado que. Just remember that if you choose to use como for this meaning, the clause must always go at the beginning of the sentence, whereas ya que can be placed in the middle as well.