MwRYum
Major
I think Russian sold many IL-76 to commercial sector as cargo plane. Many are due to be replaced because of old airframe.
Y-20 will come in handy to compete with Russian IL-476.
Primary attraction of the Il-476 is the use of PS-90 series engine, which sets to meet modern emission standard, IIRC this is what restricted current Il-76 operations in Europe because current engines failed EU emission standards.
As for competitions in this sector, commercial market for outsized cargo that needs such aircraft is a very niche one, most air cargo are flighted by cargo planes variant of commercial airliners, only when it's something that's too big to fit through even a 747 cargo doors or lifting it up high to load is non-realistic an option then you'd need such planes...typically, when something like that comes along that'd be the job for something in the grade of An-124.
Cargo planes in this weight class and with rough-field capability is primary military market, and since only major armies have such requirement and budget, that further narrows the competition.
That said, most countries who needs such planes are either in good terms with the US and rich enough to buy C-17, or would buy Il-476 if there's a budgeting concern, alas Il-476 have yet reach production phase, even when it does it's the Russian Air Force's contract that it's to satisfy, then comes other buyers.
Would Y-20 fill this gap or break the monopoly of C-17 in this very narrow market? I'd say it'd hardly so, for one unlike C-17 or Il-76 (or Il-476) Y-20 is complete unknown, so for logistical train stability picking either one of those two would be easier sell; then comes the availability of production capability of both Il-476 and Y-20, both have their launch customer's orders lined up, so unless Il-476 faces major hiccup in its production then market shares would slip to Y-20's side. Lastly, potential in commercial sector would really depends on current Il-76's airframe, of how many have clocked their maximum lifespan and slated for retirement in the coming decade.