No, it can take a few minutes. A big factor is the diameter of the pipes used to carry the hot water. See: This Old House videos on the topic. Bigger is NOT better here; a larger pipe may take several minutes to empty out of cold water before hot water starts reaching you.
In the rental house we just moved from a couple months ago, the last homeowner did several amateur projects (or hired a handyman who worked at that level). They fitted a larger, elevated water heater, but also "upgraded" the water pipes in the attic to a ridiculously large diameter. Between that and the rental property management fitting water-saving low-flow fixtures, you could turn on a hot water faucet and go boil tea on an electric kettle (or something) in the meantime. By the time you're done drinking the tea, the running water might be getting warm.