Meaning of 的 in 我十岁才到的美国
[...] after reading my grammar notebook, I think that 的 belongs to &quot;是...的&quot; structure, though 是 is omitted in this sentence. Take a look at [this resource] and focus on the part of &quot;Position of 的&quot;. It is said that 的 can be put between the verb and the object.

Your grammar notebook  correctly addressed the use of 的 in your example.
Compare to 我(是)七点到的学校,  我(是)5点下的班，etc.
Those are often heard in day-to-day conversations.
Here is more quote from dictionary definition:

（用在谓语动词后面， 强调动作的施事者、时间、地点等）:


I made the sketch; he filled in the colours.
是我打的稿子， 他上的色。
It was the year before last that he went to Xizang [Tibet].
他前年去的西藏。