Yes, a person can first स्वीकार Jain Dharma with sincerity and then marry a Jain girl, if the conversion is genuine and based on श्रद्धा, not only for marriage.

In Jain tradition, the important points are:

• Sincere acceptance of Jain values: Ahimsa, Satya, Aparigraha, brahmacharya, and respect for the Tirthankars.
• Real understanding of Jain Dharma: not just changing a label, but learning and following the principles.
• Respect for family and community traditions: many Jain families may want the person to show consistent practice.
• Marriage should be honest and dharmic: the intention should be truthfulness and mutual respect, not only convenience.

So, yes, it is possible, but the conversion should be heartfelt and the marriage should be approached in a proper Jain way. A true Jain acceptance is judged by conduct, not only by a formal declaration.