An "informal notice" may be sent to a tenant at any time. An "informal notice" is a notice that you WILL NOT use as a basis to evict a tenant or to terminate tenancy. Examples of "informal notices" include: a notice that the tenant sent the rent check to the wrong address last month, a notice that the tenant is not keeping the grass properly watered, or a reminder that parking is assigned and the tenant is parking in the wrong assigned parking space.
A "formal notice," on the other hand, is a prerequisite to an eviction action. "Formal notices" include: a 5-Day Notice to Pay or Quit (for nonpayment of rent), a 10-Day Notice for Material Noncompliance, or a 5-Day Notice of a Noncompliance Materially Affecting Healthy & Safety. A "formal notice" MUST be served upon the tenant before the landlord files an eviction action in court (called a special detainer action for residential tenants).
So, when can the landlord serve a formal notice? As soon as the default has occurred. For nonpayment of rent, assuming rent is due on the first day of the month, then the 5-Day Notice to Pay or Quit may be served on the second day of the month because rent is delinquent on the second day of the month. And this is true without regard to when (or if) late charges begin to accrue. For a non-monetary default, such as a 10-Day Notice of Material Noncompliance (i.e., for unauthorized pets, unauthorized guests, noise, etc.), the notice may be served on the same day the default occurs. You may also serve the notice "sometime after" the default has occurred, but a delay of more than a couple days (other than for nonpayment) may cause some judges to conclude that the default was not that significant if failed to act promptly.
