The best possibility for Novgorod to become Catholic would be to cut it off politically from southern Russia at an early date, and keep the mid-late C10th united principality of Russia from developing - at least until Novgorod's economic importance and autonomist mercantile elite are too strong to be just overwhelmed militarily then made to turn Orthodox by a unifying ruler based in Orthodox Kiev. We do not know much about the real history, as opposed to later propaganda-influenced Church chronicle version, of the C10th internal dynamics of Russia and how the Rurikid dynasty, originally based in Novgorod and ruling a mixed 'Scandinavian' (probably mainly Swedish) immigrant warrior elite and local Slavs ,managed to hold onto the distant North at the same time as gaining and holding onto Kiev far down the Dnieper. Probably Rurik (a shadowy and part-mythical figure like many early medieval dynastic 'founders', eg in Anglo-Saxon England) and his river-based invaders , mixed warriors and traders as usual for the 'Viking' elite, or another early leader of the 'Rus' took over Kiev by force or (as in tradition) a local 'request' by the Slav town leadership there as its protectors, around 880-900, and subsequent leaders based in Kiev (traditionally Oleg and Igor) had too large and mobile an army for the North to risk defying them.
Trade from the South and via Kiev from the Central Asian steppes and the Byzantine Empire would be cut off too by any break, so a split between North and South Russia in the C10th was too risky for the local elites - Novgorod serving as the entrepot for the riches of the South and East en route to Sweden (apart from those goods which passed via the Dvina to what is now Latvia and the central Baltic.) Nor do we know who commanded in Novgorod after the Rurikid princes moved to Kiev - was it already a largely self-governing merchant elite with the Prince or his deputy just leading the army and having to take the advice of a Council who had elected them? But after Igor's son Svyatoslav was killed on the steppes S of Kiev in an ambush in 972, following his failed war to invade and overrun Bulgaria in 969-72 when Emperor John Tzimisces of Byz evicted him, Russia split up among his three sons and it was late in the decade before his youngest son Vladimir, at first based in Novgorod. reunited Russia; V then converted himself and his people to Orthodoxy after his war with Byzantium in the Crimea in 988. (He had been refused a promised Byz princess as his wife so he marched on and conquered the Byz Crimean province centred at the port of Cherson while emperor Basil II was distracted by a civil war; B had to give him his promised wife and agree an alliance to get it back, and hired the first Russian mercenary 'Varangian' regiment for his army to win the war. Conversion to Orthodoxy was part of the deal.) If the civil war in Russia ends in stalemate with Kiev holding out in 972-9 and Vladimir is defeated or restricted to the North, Russia stays split up and might remain so for decades - giving the nervous Novgorod elite time and reason to align to the Western European powers , most probably through a Swedish alliance involving military aid against Kiev, and show their goodwill by accepting Catholicism to get the Pope on side. The Papacy would then be willing to back up Novgorod and could get its close ally , the Holy Roman Emperors Otto III to 1002 and then Henry II, to send troops if N is attacked. Given long-time Novgorodian autonomist behaviour, Novgorod is less likely to accept help from the expansionist (and newly-created) Polish state which as of the 980s was still pagan anyway and was a local rival of the new Russian settlements/ embryonic principalities in Volhynia / Pinsk (modern NW Ukraine and Belarus); the Holy R Empire was further away, busy fighting the pagan Swedes and Prusssians in what is hnow N Poland., and less likely to try to swallow up its new Novgorodian ally.
If there is no Byz civil war in the 980s - eg by John Tzimisces not being assassinated in 976 and his ward and titular co-ruler, the young Basil II (born 958), not being challenged by JT's relative Basil Sclerus and the Phocas dynasty too - there is no liklihood of a Byz/ Russian clash over Cherson and the subsequent conversion of Vladimir and Kiev to Orthodoxy following at that date. But the Byz clergy had developed a Slav Church liturgy and translated Bible and were interested in converting the Slavs, so following up their missions in Bulgaria in Russia was a logical path to follow - and converting the Rus would 'tame' them and stop them attacking the Empire, as they had done in the 940s and late 960s; Svyatoslav's mother (St) Olga/ Helga had already visited Constantinople on a diplomatic visit as regent in the 950s and converted with some of her elite. Conversion of the ruler of Kiev was a probability for the late C10th or early C11th (dates according to how preoccupied Byz and the Kiev ruler were) though there was always a chance of a Russian ruler gambling on turning Catholic to get Papal help instead out of fear of Byz power. (The Bulgarian ruler had briefly done so in the 860s but been persuaded to turn Orthodox instead by the threat of the Byz army invading.) Or the quirky and autocratic Vladimir could have even turned Moslem to ally with the Russians' trading partners in Central Asia, the Samanids of Khorasan - though as alcohol would be banned this is less likely. Long term, keeping the Russian states split between two powerful warlords and their heirs in N and S is Novgorod's best chance to turn or stay Catholic , esp if a different steppe trajectory sees a Kievan victory over the Polovtsian/ Cuman nomads on the lower Dnieper and greater settlement and interest in the steppes , linked to trading towns on the Black Sea, than in the poorer agricultural land of the forests of the North. Then we would get two different lines of Russian development - until the Mongols arrive in 1240 and Orthodox elites in Kiev flee North and take over Novgorod as a safer refuge in the woods and marshes?
