We can certainly estimate the lower bound on the timing of Pandava’s अज्ञातवास, with the help of one reference from Stri Parva (स्त्री पर्व ) of Mahabharata text.
On the day after the last and 18th day of the War, Utttra, wife of Abhimanyu, states…
GP edition Stri Parva 20:28
एतावानिह संवासो विहितस्ते मयासह
षण्मासान सप्तमे मासि त्वं वीर निधनं गत:
</strong<strong>>(My brave Abhimanyu, You could only spend 6 months with me in this world. In this 7th month, you attained death in the battlefield.)
Abhimanyu died at the end of 13th day of the War. This day, per my proposed timeline is that of 28 October 5561 BCE.
Since we do not know how much of the 7th month (that Uttara refers to) had elapsed, we will go back by only 6 months from 28 October 5561 BCE.
Going back by 6 lunar months (synodic lunar months), we arrive at 4 May 5561 BCE. Sun was at the point of Spring equinox on this day (one day after spring equinox).
We may thus state that Pandava’s वनवास (stay of 13 years in wilderness) did not begin anytime after the spring season. This is of course based on the assertion that Luni-Solar calendar along with seasons were employed in keeping track of Pandava’s time in वनवास.
Thus Pandava’s अज्ञातवास (incognito interval) ended sometime at the beginning of spring season.
Researchers who are curious about 13 years of Pandava वनवास and problems associated with it may use above assertion (i.e. Pandava वनवास did not begin anytime after the spring season)in exploring this subject further.