However, Alex Revell's Boro will be coming into the game with more confidence than they might have done, following their first win in two months earlier this week.
Hull City were a Premier League team as recently as 2017, when they finished in 18th place and were relegated.
Founded in 1904, the Tigers spent five seasons as a top flight club, having reached the 2014 FA Cup Final and competed in the Europa League during this time.
They moved from long-standing home Boothferry Park in 2002, to what is now known as the KCOM Stadium.
Since relegation, City have struggled, dropping down to League One for the first time in 15 years as a result of relegation from the Championship last season, finishing in 24th place.
After their rousing 2-1 victory over Port Vale, which included strikes from the talented QPR loanee Aramide Oteh and the lively Danny Newton to propel Revell's side out of the relegation places, Boro are hoping to add Hull to their list of FA Cup scalps and make the hat for the prestigious third round draw.
Boss Revell hailed the 'intensity and 'desire' his side showed in the midweek triumph - and will be hoping for more of the same again illustrious opponents, that reached the 2014 FA Cup final, only to be narrowly beaten by Arsenal 3-2 after extra time in a classic Wembley showpiece.
Grant McCann's team from Humberside have impressed this term with only three defeats from 13 league matches after their dispiriting relegation from the Championship last season.
The Tigers have the best away record in League One, boosted Tuesday night's 3-0 win at previously unbeaten Ipswich Town.
The Stevenage squad has few injury issues to report. Only Jack Aitchison and Elliot Osborne (ankle) are out of contention.
Ones to watch
Oteh and Newton excelled against Vale, but there were a raft of players that performed at the level they are capable of, one that accurately represents their talents.
This included the acclaimed Luther James Wildin, as well as the solid centre-back pairing of gnarled veteran Scott Cuthbert, and the uncompromising Luke Prosser.
Charlie Carver is a talent waiting to explode, while Jack Smith is becoming an influential presence, certainly if his excellent outing against Vale is anything to go by.
Hull for their part, as befits the table toppers they are, also have excellent players who are flourishing under McCann, including Josh Emmanuel, Jacob Greaves, Mallik Wilks and Josh Magennis, with George Honeyman being the standout performer so far.
Head to head
Stevenage and Hull City have never met before
Referee: Sam Allison
Assistant Referee 1: Alistair Nelson
Assistant Referee 2: Aaron Farmer
Fourth Official: Robert Whitton
How to watch Stevenage vs Hull City
It promises to be an exciting game, which explains why the BBC will be broadcasting the clash, which kicks-off at 1:30 pm.
Sunday's second-round clash will be broadcast in full across BBC iPlayer and the BBC Sport Website/App.
Live video updates will also be shown on BBC Final Score throughout the afternoon.