You can start a ULIP plan at any age, provided the age falls under the minimum and maximum age limits of the chosen policy. Many ULIPs allow coverage from 3 months onwards. The maximum entry age, however, is limited to 65 or 70 years depending on the features of the plans. This may differ from Insurer to Insurer.
So, you can start a ULIP within the minimum and maximum age bracket.
That said, it is better to start ULIP as early as possible so that you can opt for a long-term tenure and also save affordably to create a corpus for your financial goals.