Never.
It's not a Catholic Mass, and it's almost certainly invalid.
Pope Leo XIII declared in Apostolicae Curae that the removal of nearly every reference to the priest's power to sacrifice rendered Anglican Holy Orders invalid even if the essential form were correct (or corrected, as some tried to do), and that's due to the "intention of the Rite" itself, which was made in order to accommodate the "errors of the Reformers". That's admittedly what they were doing with the NOM, and the Prots famously collaborated in it, with one of them saying he'd have no qualms of conscience using it. That's the "intention of the Rite", which Pope Leo XIII declared invalidates a Rite. WHY, historically, did it come into being? To accommodate the Prot errors.
Most importantly, if a priest were to use the "Eucharistic Prayer I", largely the Roman, and you dressed it up like the Latin Novus Ordo at St. John Cantius, while outwardly you coudln't tell the difference, there's one fatal flaw that's not been given sufficient attention even by critics of the NOM, missed even by Father Cekada.
THE OFFERTORY
Father Cekada said the NOM has no Offertory. That's incorrect. It most certainly does. But they changed WHAT is being Offered in their "service".
So, if you just go through the "Eucharistic Prayer", aka Canon, many other Prots do the same thing. But what are they doing? For many it's just the "institution narrative", where they're just re-ENACTING what Our Lord did at the Last Supper and told His followers to do likewise.
It's actually the OFFERTORY, in the Catholic Mass, that explains what the Church says is taking place here, where the Spotless Victim (Latin Hostia being a technical term for an animal blood sacrifice) is being offered for sins. That is what the Mass is, and it's only explained clearly and unequivocally in the Offertory. Remove the Offertory and you can spin it as anything you want, and even the word "sacrifice" by itself means nothing, since that just means making something holy, and its even use in terms like "sacrifice of praise".
In the NOM, the Catholic Offertory was replaced by a Jєωιѕн table prayer (almost verbatim), where they declare that they are offering the bread and wine, the "fruit of the earth" and "work of human hands" ... so it can become some kind of "spiritual drink" (whatever that means).
So, do bread and wine expiate sin? Or do anything at all?
This was done on purpose, folks. So, where have we seen those expressions "fruit of the earth" and "human work" before? They sound familiar. Oh, yeah, it was Cain who offered up the "fruit of the earth", and it was rejected by God, vs. Abel's blood sacrifice (of an actual "hostia"). People have asked about why Cain's sacrifice was rejected by God. One answer is, where St. Paul explained, lack of right faith. But the other reason is that ... if you look at Adam's punishment for Original Sin, God declared that "cursed is the earth in thy work".
So the Novus Ordo Mass is offering to God the "fruit of the earth, work of human hands", when God has declared "the earth .. cursed ... in [human] work"?
We replace offering the Hostia, the Victim, with offering the cursed punishment for Original Sin? Yeah, don't think that's going to do much more than incur God's wrath.
And, the offering is almost verbatim a Jєωιѕн table prayer.
Our Lord had complained to Marie-Julie Jahenny that "those who crucified Me" were perparing a New Mass that was "odious" in His sight and contained "words from the Abyss". Hmmm. Those that crucified Him, the Jews, introducing Jєωιѕн table prayers to replace the Catholic Offertory ... could those be the "words of the Abyss" to which He had referred? What else could that be? Reducing the number of Kyrie Eleison / Christe Eleison?
Also, Catherine Emmerich foresaw a new Church in which their Eucharist was invalid, but that God would reward some who devoutely attend it with some graces, but not because of a valid Sacrament, basically, ex opere operantis vs. ex opere operato from a valid Eucharist.
So, no. We can never attend the Novus Ordo (except passively for the usual reasons we might attend other non-Catholic Rites). We cannot actively participate. It's not a Catholic Mass.
And just because groups like St. John Cantius tried to put lipstick on that pig doesn't make it a Catholic Mass. It's the Offertory, stupid! If they had not removed the Offertory, I would say that it might be OK if done like below at St. John Cantius in Chicago ... and almost certainly valid if offered by a valid priest. But I hold that it's almost certainly invalid ... even after they fixed the English mistranslation of the form.
Don't be fooled by this. Many Motarian groups are accepting the Novus Ordo in Latin as a replacement for the Tridentine Mass (including a couple in my area), and most don't know the difference ... but that's becaue they're all about the smells and bells and not the substance.