"first several years" is correct and usable in written English.
For example, you could say, "The first several years of our marriage were filled with fun and laughter."
Her first several years were hard.
Adaptive skills comprise the most important developmental tasks accomplished during the first several years of life.
The award will also help fund his first several years of research at MIT.
Human brains develop at a staggering rate during the first several years of life.
In the first several years, Ms. Alexander struggled to find a permanent space.
The plan would have positive effects in the first several years.
In his first several years, he ran a sort of in-box operation.
First, several years ago, there was St.-Germain, the delicate elderflower liqueur.
I spent the first several years of my life on expedition with my parents.
But despite initial heavy marketing, the channel generated significant losses in its first several years.
For the first several years, he designed a miscellany of minor buildings: lofts, garages, even outhouses.
