Very hard, as even in the best circumstances there is simply not enough ethnic/cultural Finns and Estonians to be an Italian sized economy.
I'd start with the Livonian Sword Brothers as some have already stated. They are not defeated at the Battle of Saule in 1236. They avoid defeat and expand east along the Daugava River. They retain their independence and are not subsumed within the Teutonic Knights.
Over the next decades, the Sword Brothers expand north and east into more Finno-Ugric territory. They defeat the Novgorod Republic in a great battle in the mid 13th century. They gain the city of Pskov and advance north into Ingria. Future wars continue to push the border east, and the Sword Brothers are able to expand into Karelia and Finland. The Livonian Sword Brothers become an order state predominantly situated over Estonian/Finnish speakers.
The collapse of Mongol power in Russia allows the Sword Brothers to expand again basically conquering all of Novgorod lands and other lands along the Daugava River, taking Polotsk and Vitebsk.
By good luck and some able grandmasters, the Sword Brothers order-state survives and prospers. The order increasingly relies on local Estonian auxiliaries to support the monk-knights. IOTL, Lithuania managed to expand deep into Russia in the 14th century, ITL it is the Sword Brothers. Possibly, they even succeed in incoporating ethnic Lithuania into their state.
When the reformation happens, the order secularizes and turns itself into a normal government and aristocracy. War with Sweden allows the order to conquer all of Finland, uniting most of the native speakers of northern Finno-Ugric together. Rise of native Russian power causes the Livonians to lose some power, but they stabilize the border and able to contain the incipient Great Russian state. Crucially, they form a border which retains the cities of Minsk, Tver, Smolensk, and Moldova.
The spread of western agricultural technology and crops cause a population boom of Finnish and Estonian speakers who eventually dominate the less sophisticated slavs in the northern interior who adopt the techniques and crops at a later date. Eventually, the German speaking upper class change to speaking Estonian at this time, much like the Norman and French speaking nobility of England eventually adopt English.
This super Livonia defends itself against the Swedes, Poles, and Russians. They lose some of the higher populated lands of Lithuanians and Russians, but keep and expand into the land we would consider NW Russia. The state increasingly identifies itself as an Estonian/Finnish people with sizable slavic minorities. The country is heavily dependent on grain imports from Poland, the Ukraine, and trade across the Baltic, but compensates by the fur trade and maritime trade.
During the rise of nationalism, Livonia renames itself Estonia, declares all speakers of northern Finno-Ugric to be speaking dialects of Estonian, considers itselt to be the nation-state of all Estonians, and the elites begin to spread education of a standard Estonian language, literature, etc. This alienates many of the remaining slavs in their lands, but also succeeds in Estoniazing many of them, especially those who live in areas where Estonian speakers already dominate.
Estonia has missed out of the colonial empires, but it's emphasis on trade turns it into a Baltic, Barents, and White Sea Netherlands. This makes Estonia very rich, and they are able to hold onto their land in wars against the larger populated Slavic states to its east and south.
The area we call Estonia would include OTL's Estonia, Latvia, Finland, a northern slice of Belarus, and much of NW Russia and Russia's northern coast. It is heavily dependent on food imports, but has a rich trading culture and known for its engineering skill and high tech products and computer services.
Historically, it's been the great power of northern Europe, but lost that status first to a united Scandinavia (which is its equal), and the far heavier populated Russia (with its capital at Kiev). Nowadays it is no longer a great power, but remains a wealthy and prosperous European state.
