I was pretty confident that animal companions could use all their primary attacks until I thought about it in the context of the Multiattack feat. Can an animal companion do so before obtaining this feat? If so could you point me to the RAW?
Yes, Animal Companions get all attacks listed in their stat block (primary and secondary) starting at the level that lists them.
The animal companion's Multiattack ability (granted at 9th level) states,
The Multiattack feat itself says,
In other words:
Note that some animals have 3+ primary attacks and no secondary attacks (e.g. the Big Cat). Because all three are primary, they get no penalty to hit on any of their three attacks, even at 1st level. At 9th level they'll gain the Multiattack feat...but it won't actually help them. While this may seem a bit odd it's clearly the way the rules work...and I wouldn't shed a tear over it because animals with 3+ primary attacks are probably already great companions.
Since you asked "could you point me to the RAW", see Monster Entry Format in the Rules for Monsters section, which says,
I think that's the closet the rules get to saying "Creatures get access to anything listed in their stat blocks (including any attacks)".
EDIT: As KRyan noted in a comment, people often forget that creatures only get all the attacks as a Full-Attack. On a standard-action Attack, they only get one attack. (This is true for Animal Companions...and any other creature with multiple attacks, unless its rules text explicitly allows it to do more on a standard-attack.)
EDIT 2: User highbandwidth asks in a comment how one knows what are Primary vs Secondary attacks. The general rules are in this table (so cats, badgers, and anthing else with claw/claw/bite have only primary attacks).