Q. Can a Bar Mitzva boy that following family tradition puts on Tefilin thirty days before his Bar Mitzva and that falls in Chol Hamoed Pesach, put them on then without a brocho?
A. On a similar question (1033) as follows:. “Following our minhag my son should put on tefilin first time thirty days before his bar mitzvah and that would be on Sunday, the Isru Chag of Pesach. Due to the fact that the family will be together during Yom Tov, can he put on tefilin first time on Chol Hamoed (our minhag is to put on tefilin in Chol Hamoed without a brocha) and make a seuda then, when all the family is home? Should he make then sheheyanu on his new hat and the tefilin?”
We answered: “We find in many mitzvos, events and occasions that the beginnings are vital and crucial. From the Bereishis of Creation, the Rosh Hashono of every year, the “shono rishono” (first year)of a marriage and many others, whatever is built after, stands on the foundations of the commencement. As the well know maxim teaches “everything follows the beginnings”.
Therefore, Horav Shlomo Miller’s Shlit”a opinion is that this most important event of donning tefilin for the first time, should be done at a time when the mitzvah of tefilin is undisputed and can be said with a brocho, as opposed to your minhag during Chol Hamoed. See question # 918 on this forum in regards to reciting sheheyanu on new tefilin”
In your case it would be reasonable that he should begin donning Tefilun with a Brocho before Yom Tov begins.