Information under Art 13 (data obtained directly from the data subject) must be provided at the time when the personal data is being obtained. Since most websites will obtain personal data pretty much continuously, they will likely have to keep this information available continuously as well.
Information under Art 14 (data obtained from other sources) must be provided within a reasonable time after obtaining the information, but at the latest when the data subject is contacted.
However, all such approaches stink. Doing the bare minimum that's explicitly required is an easy way to run afoul of more foundational GDPR principles, e.g. the Art 5(1)(a) requirement that all data processing must be transparent (compare also Art 12(1)), and the Art 5(2) accountability principle: the data controller must be able to demonstrate how what they're doing is compliant.