As Grigory already said, master links for 8 and 9-speed chains can often be opened or closed by hand. I believe this is because the clearances between the chain components (e.g. the pins and rollers) are larger than on higher-speed chains.
One minor thing about the original question struck me: the poster referred to pedaling their bike upside down. This makes me wonder if they tried to re-install the quick link with the bike upside down as well.
Looking at the bike upright, the top span of the chain (i.e. the span running from the chainring to the cassette that's sitting above the chainstay) should be (to my mind) the one that's responsible for transferring your pedaling force from the crank to the cassette. Adam Kerin, who has extensively researched the friction producing mechanisms in chains, indeed implies that the top span is higher tension than the other spans (bottom of pg 2 of this document).
In this YouTube video, David Rome of Cyclingtips recommends that if you aren't using a specialized tool, you can (with the bike upright!) backpedal so that the quick link is in the top span of chain, put the bike on the ground, activate the brakes, and pedal forward. The link should then snap into place. If the bottom span of the chain were under equal tension as the top, then it might not really matter where the quick link was positioned when you start pedaling. In any case, to ensure that the link is properly closed, I would use this procedure.
Relatedly, we often recommend that people not put their bikes upside down to service them if possible. Aside from possibly scraping some components, I haven't heard a solid rationale offered for this. However, if you invert the bike, the span of chain under full tension when you pedal should now be the bottom span (from the perspective of the bike when upright). Often, when doing this as a quick fix, I have later found shifting issues that presented when riding but not with the bike upside down. I suspect that one contributing factor is that the chain is being tensioned differently than when under normal operation. Also, pedaling by hand obviously produces much lower torque than actual pedaling, so you might expect that this could hide some shifting issues as well.