I saw in one of the answers that one may pour hot water from a Kli Shlishi onto ground coffee so it will drip through and make coffee. My understanding was in order to do this, the coffee must be set up in the filter before the onset of Shabbos. Is this correct? Thank you.

Shalom, The question of using a coffee filter on Shabbat involves two issues. The first is the issue of straining liquids on Shabbat through a strainer. As you read in the answer of Rav Blass, there is good reason in the case of coffee filter use to allow this. The second question is one of cooking on Shabbat. There are many opinions about the permissibility of cooking coffee, even roasted coffee beans, on Shabbat. However many people hold by the opinion that water in a third vessel does not have the ability to cook the coffee, and would allow using such water to pour over the coffee into the filter. This does not need to be set up before Shabbat, and the coffee may be put into the filter and placed over the cup on Shabbat itself, and then the water poured into it from a third vessel. The use of an electric coffee machine is much more problematic. Most Rabbis prohibit using an electric coffee maker even if it was set up before Shabbat to turn on automatically. Even those who do permit using such pre-set machines generally require the coffee to be set up in the filter from before Shabbat, as you wrote. Blessings.