Are there optional squad members in Mass Effect 3?

Javik the Prothean is a DLC only squad member that's available in the "From Ashes" DLC:

Access to From Ashes is included free with all copies of the Mass Effect 3 N7 Collector's Edition and the Digital Deluxe Edition. It is available for purchase separately for 800 Microsoft Points, 800 BioWare Points, or $9.99 USD on PlayStation Network.

And as @LessPop mentioned, the events in previous Mass Effect games will mean that there will be some squad members that are completely unavailable in the game:

Ashley/Kaidan depending on choices in ME1, and Garrus and Tali depending on their survival of the suicide mission in ME2.

Other than that, the only way to 'miss' a squad member is to follow certain decisions in ME3 which results in their death. There's no way to avoid recruiting any of the non-DLC squad members in ME3, they all show up as a part of the main quest.

You will always have the Virmire survivor on your team in the game's early mission to Mars, before you assume full control of the ship. After that, they won't be around for a while and it is totally optional to allow them back on your ship again or not.

Garrus and Tali are optional in that they could both be dead from ME2. Also there is a way to tell Tali to not join you....I'm not sure that option is there for Garrus though. However, both of those characters will still join you shortly after their introductions, no matter what, as you are required to take them on the missions right after you first meet them. Tali's option for dismissal happens AFTER the initial missions you're required to bring her along for.

Liara, EDI, and Vega are not optional, as far as I understand. They represent your squad's biotic, tech, and combat basics.

Javik is totally optional.