The Torah clearly stipulates what offerings God's people are to make in atonement for sins, but what was the status of those people after they had sinned (providing it was not a sin worthy of death) but before they were able to get to the temple to make the offering? Were they considered unclean, and if so, did they go to the Temple to make offerings often, or during the times that they were commanded according to the law?
With very few exceptions, sacrifices are for inadvertent violations which can include violations which would have had a death penalty had it been on purpose and with witnesses and warning - for example a Shabbos violation. If the person forgot what day it was, or forgot that the specific activity was forbidden, they would have to bring a sacrifice. (Rambam Sheggagos 1:1).
The sacrifice was brought when they could get to the Temple, which would be expected on one of the three holidays of Pesach (Passover), Shavuos or Sukkos. It is a requirement that it be brought at the first one after the person becomes obligated, and failure to bring them after three have passed is a violation of an additional commandment. (Talmud Rosh Hashana 4a (at the bottom), Rambam Maaseh HaKorbanos 14:13).
Interestingly the Rambam doesn't specifically list sin offerings as subject to that issue, but I didn't see anyone comment on it, nor did I find the Rambam said anything else (but maybe I missed that) and it is specifically part of the list in Rosh Hashana.