Yes, it's possible for an INTJ to show their playful and child-like side when they are interested in having a relationship with someone. While INTJs are known for their logical and serious demeanor, they can also exhibit more lighthearted and playful behavior when they feel comfortable and close to someone they care about.
When an INTJ is interested in forming a deeper connection with someone, they might allow themselves to let their guard down and reveal a more fun-loving, spontaneous, or playful side of their personality. This can include engaging in humor, making jokes, playfully teasing, or participating in activities that they find enjoyable and entertaining.
However, it's essential to recognize that each individual's behavior varies, and not all INTJs may express their playful side in the same way. Some INTJs might be more reserved even around people they are interested in, while others might be more open and playful from the beginning.
Additionally, the extent to which an INTJ shows their playful side can also depend on their level of trust and comfort with the other person. Building a relationship with an INTJ often involves earning their trust and creating a safe space where they feel free to express different aspects of their personality, including their more playful and child-like qualities.