Legal systems shape not only the recognition of migrants and refugees but also the pace and stability of their integration. Refugees often shift between multiple legal classifications, a process we refer to as the "legal journey". This journey is frequently prolonged and uncertain. Using a network-based approach, we analyze legal transitions for over 350,000 migrants in Austria (2022 to 2024). Refugees face highly unequal pathways to stability, ranging from two months for Ukrainians to nine months for Syrians and 20 months for Afghans. Women, especially from these regions, are more likely to gain protection; Afghan men wait up to 30 months on average. We also find that those who cross the border without going through official border controls face higher exit rates and lower chances of securing stable status. We show that legal integration is not a uniform process, but one structured by institutional design, procedural entry points, and unequal timelines.