Paul Pierce's baby mama Princess Santiago isn't hiding out after the former NBA All-Star's bombshell admission ... and she's got the child right by her side.

Santiago was spotted out in Beverly Hills on Tuesday for the first time since Pierce admitted to being the father. She was seen grabbing a bite at an outdoor restaurant ... calmly cradling her 2-month-old son King Rafael Santiago Pierce as the custody battle with Pierce plays out behind the scenes.

The vibe was low-key and all about mom duty. In the pics, she keeps things intimate, holding the baby close and even leaning in for a sweet kiss ... clearly locked in on her newborn despite the headlines swirling around her.

As we previously reported, Pierce admitted last month he's the father and is asking for joint legal and physical custody. Santiago, meanwhile, is pushing for sole custody -- along with nearly $30K a month in child support and additional expenses.

She first filed a paternity suit in California back in January. She's made sure to highlight Pierce's massive NBA earnings -- claiming he pulled in close to $200 million during his career -- as justification for the sizable monthly ask.

But at least on this outing, there's no sign of stress ... just a new mom focused on her child while the off-court drama continues to unfold.