Is there a minimum amount of time in Canada before an H&C application makes sense?

There's no fixed minimum period of time in Canada required before you're legally allowed to file an H&C application — it can technically be submitted at almost any point. Whether it makes practical sense sooner rather than later is a different question, and it depends heavily on how strong the supporting factors actually are at the time of filing, particularly establishment, which generally builds meaningfully over time.

Filing very early, before meaningful ties, community involvement, or other H&C factors have had a chance to develop, often means the application has relatively little to work with, since establishment in particular tends to be one of the more persuasive factors and is inherently time-dependent. On the other hand, waiting indefinitely isn't necessarily better either, especially if other circumstances, like an approaching removal date, make timing urgent regardless of how developed the file looks.

Because the right time to file depends on weighing the strength of your current evidence against your specific circumstances and any time pressure you're under, this is a decision best made with legal advice rather than by rule of thumb, since filing too early can mean a weaker application while waiting too long can mean missing the right window entirely.