Goebbels offered the solution to this problem in 1929:

One ought not to afford to the Jew in the struggle the means that one affords to every honest opponent; for he is not an honest opponent; he will merely exploit magnanimity and chivalry to place his enemy at a disadvantage.

You say "I know you're lying, you know you're lying, so fuck off." to any chink virus hoaxers.

Getting to zero new cases isn't as difficult a quandary as you make it seem, this all comes down to reproduction rates that's what all this is about. If while a person is infected they spread it to two people the virus has reproduced twice, lets say that's normal for this virus, that would be called an R0(rate of reproduction) of 2. To make the virus go away we need to keep it below 1 R0 for long enough for it to die out. People with immunity to a virus can't spread it generally so when enough people are immune the virus naturally slips below R0 1 and disappears over time. This is why vaccines for diseases once common everywhere, but that still exist outside of the developed world, work so well in preventing outbreaks in the developed world even though most of these vaccines were only about 90% effective when they were first distributed and since then are likely as low as 70% effective, possibly much worse, they work because each infection actually prevented represents a theoretical reduction of R0, this means if an infectious person encounters 2 people who are both vaccinated and the vaccine is only 50% effective to that strain of the virus one will get sick and the other wont, or both could be sick but for half as long the result is that the R0 of 2 has been effectively reduced to 1 meaning rate of spread is halved what it would be without medicine, if while infectious the infected people stay home they reduce the likelihood of spread by nearly 100% if they must go out and wear a mask while they do that will reduce the spread by over 25% if worn properly, another ~25% if they also keep a fair distance from others, turn their head down to cough or sneeze that will reduce likelihood of spread and if everybody washes their hands more frequently, sneezes into their elbows, and touches their face less that would also mitigate against spread.

So if the disease has an R0 of 2 and we don't have any immunity to make it disappear we need to mitigate spread by 51%, universal masking, social distancing, and maybe more hygienic practices and a sense of caution to encourage hand washing should put us over 50% but if we half ass it and only get to 49%, yeah we've slowed spread but also created a situation where if prolonged we are more likely to see the virus become more infectious via Madurai selection because not enough immunity exists yet but eventually we'll hit a tipping point where immunity from infections nudges us over 51% and drags the virus under an R0 of 1 if this happens in warm months the virus will likely disappear so long as we continue taking all of our mitigative efforts, too many get lax and it will tip back the other way and start multiplying again.

We don't know COVID19's natural R0 but we know it's higher than flu. The estimates I've heard are R0 ~5 and R0 ~3.4 respectively and since they spread in basically the same way most viruses do they should both be equally effected by mitigative efforts. There are four different flu viruses I know of with probably hundreds or thousands of strains each, though most strains are similar to other strains of their kind what makes these different diseases flu is their seasonal nature and low mortality rate but still significantly higher mortality rate than a common cold, the designation of flu and cold are laymen terms and sort of useless and counter productive in a purely scientific discussion but I'll continue to simplify the issue.

If you mitigate an R0 of 5 by 50% it is still an R0 of 2.5, but mitigate a 3.4 by half and it's just 1.7, if you achieve 71% mitigation the R0 3.4 drops just barely below 1 and begins to disappear if nothing changes it will disappear in as soon as 4 weeks, more likely 8 or 9 weeks possibly many more it will disappear faster the more you mitigate spread, but that 5 R0 virus is only mitigated down to a 1.45 R0 at 71% mitigation. You need 81% mitigation to make it start to disappear. 81% is unlikely to happen from just washing hands, wearing masks, and staying home but they would slow spread and therefore mutation enough for a vaccine to still be effective against most if not all variants.

If you tried hard to get to 81% mitigation without immunity you would need perfect or near perfect obedience to all mitigative measures those being: universal masking social distancing, self quarantines, alerting potentially infected people that they might be infected or carriers and should begin a round of prophylactics for a whole week, distributing effective therapeutics to shorten the disease's life cycle allowing society to function as normally as possible most of the time, regional lockdowns in highly effected, dense population zones, remote work and education when possible, proactive hygienic measures like washing handles in public spaces, installing better air purification systems which uses light to kill viruses passing through, putting up physical barriers for people who work at tills or in similar situations encourage religions which can do remote services to do them as often as they can, try not to inflame or instigate social unrest, set size limits on gatherings, close entry into the country with few exceptions. If you do all that faithfully and with commitment you will probably crack 81% mitigation and just need to hold like that for about 2 months, if you were to pick a time to undertake such an endeavor it aught to be summer for a number of mitigative reasons, from there setting up regional ballast zones to contain future infections that may come from ports of entry essentially a quarantine protocol where regions around ports, air ports, and common border crossings become like air locks to prevent outside spread. Think about how much of that happened here or has been halfassed for various reasons and then then contrast our situation with japan, south korea, and new zealand to name a few, where we halfassed or failed to imagine they achieved and enforced solutions.