This is a weighty question that requires a weighty response but there has already been alot of work done on this so I will direct you to that work.
To try to give you a short answer, yes and no.
Nietzsche talks about these two ideas called the Apollonian and Dionysian.
Our society heavily leans Apollonian which means we're ascendants. When trying to find meaning, we lean towards the spiritual, towards a higher plain. We want to rise up, be cleansed, and use our intellect.
The Dionysian is descent. It is soulful not spiritual. It needs to go down, to feel, to touch, and to get dirty, while there is a quality of the human spirit that wants do the opposite and rise up.
Our society is increasingly becoming Apollonian which explains why Rituals and Rites of Passages are disappearing.
Ritual and Rites of Passage are Dionysian.
And we have been mistaking Rites of Accomplishments (bettering our selves/rising up/ascending) for Rites of Passages and they are totally different.
There are many types of rituals and rites of passages. The ones that are particularly important to a man's life are rituals and rites of passages that are suppose to heal or be transformative.
The characteristics of a proper ritual that is transformative or is to heal requires that you 1) enter into a different space, you have to cross a threshold, you have to separate 2) you have to be challenged or go through an ordeal or make a sacrifice (the descent) and then 3) you have to return transformed. And 4) they can be communal which gives a sense of shared identity and purpose of men in the same tribe.
So to answer your question, getting your first car seems like a rite of accomplishment (Apollonian), whereas besting your father at something or, and it may not be politically correct to say, killing someone or going off to war (being separated, going through and ordeal, and returning) transforms us as men (Dionysian).
There is a good book on this called Re-enchanting the Forest. It talks about the importance of rituals and how we need to be mindful about incorporating rituals and rites in our lives even as we get older, and how we should be incorporating rituals and rites into the lives of our sons.
If you want to listen to a podcast on this subject, to get more familiar with the subject, listen to this:
#505: A Man's Need for Ritual - The Art of Manliness - Omny.fm