As per DP, before taking birth as Ram Vishnuji went to Goddess ParaShakti's Dham. He asked her, yow will I be able to kill Ravan? As long as you reside in Lanka, no one can defeat him.
Devi answered, when Ravan will insult one of my Vibhutis Sita, at that time, I'll leave Lanka & go, after that you'll be able to defeat him.
When Hanumanji went to Lanka, he saw Devi's temple. He went there, told her, the time for her to leave Lanka has come. Devi answered him, she was waiting for his arrival only, she left Lanka after that.
It's not only Vrinda's curse but to kill Ravan too Ramayan happened.
Shivji too helped Ram, in his anshavatar as hanumanji to unite with Sita. There are many factors combined responsible for Ramayan.