In our study, it was recommended by our professors to set a deadline and if at least 20% of the total population has responded within the time allotted, we may proceed with data analysis and interpretation. However, we cannot find a reliable source to support this method.
It sounds like this is an online survey. If so, you could take a look at Dillman et al., Internet, Mail, and Mixed-Mode Surveys: The Tailored Design Method.
Results are liable to be highly biased. Those who respond and respond quickly may represent a stratum or subpopulation which may be quite different from the unknown population in general.
If you have good covariate data, you might use that. See "Comparing Alternatives for Estimation from Nonprobability Samples," by Richard Valliant, December 2019, Journal of Survey Statistics and Methodology 8(2),
DOI: 10.1093/jssam/smz003
https://doi.org/10.1093/jssam/smz003
https://www.researchgate.net/publication/337950671_Comparing_Alternatives_for_Estimation_from_Nonprobability_Samples
However, that seems unlikely.
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