No, we are not born with any sense of critical thinking. We are born only with our material sense perceptions. However, upon recurring sensual perceptions, and as a result, subsequent conception of the first abstract thoughts in human mind, the ability to think and reason emerges.
'Unity' (or 'identity' or 'sameness') and 'difference' are the very first two abstract thoughts that the human young forms. They emerge after recognition of differences or similarities among sensory data that we absorb. Comparison between these sensory data allow us to categorize their differences under new abstract thoughts such as 'size', 'color', 'shape' from which we differentiate concepts like 'length', 'depth', 'width', 'long', 'short', 'big' ,'small', 'red', 'blue' etc. Or 'weight', 'heavy', 'light', 'soft', 'rough', 'stinky', delicious', 'sweet' etc as thoughts inferred from data absorbed by sense of touch, smell, and a subsequent recognition of their distinct qualities.
It is these emergent abstract concepts that make us capable of rational thinking (e,g reasoning, analysis, negation, etc). Because all rational thinking requires these or other abstract concepts. Besides comparison, association is among the most primitive thinking process that humans develop. A new born baby soon establishes relations between the warmth of his/her mother's arms and feelings such as sense of security and hunger satisfaction. But upon negation of these perceived relations, he/she discovers new relations between phenomena such as certainty or uncertainty, hope or frustration, achievement or non-achievement etc. However these new concepts are usually permanently established after adequate recurrence of their underlying experiences.
The toddler will soon have the ability to reason that "Mom's arms sometimes mean milk" therefore "Not all mom's hugs mean milk; they may sometimes mean kiss." This is how a kid gradually develops ability for logical/critical thinking.