In the last 40 years, 28 different coaches can lay claim to a national title. Of those, Bill McCartney is the only one who didn't have a winning record in his first three seasons. Many on this board would even argue he doesn't count since WE won the national title that year.
Other than Bill McCartney, only 2 other coaches didn't have double digit wins within their first 3 full years. Don James and Lavell Edwards. Both of which did have 9 win seasons before their first double digit win season though. In fact nearly every championship coach wins a title within the first 3 years, most are double digit wins within 2 years.
Beamer's success (without a national title) was the exception, not the rule.