Despite the expected upheaval in the transfer window, which has become a recurring theme in West London these days, the Blues have won all three games played so far.
They opened their Premier League season with a 3-2 away win against local rivals Fulham, before edging a seven-goal thriller against Brighton.
Those two matches sandwiched a 2-0 Carabao Cup win against Luton Town, and have already given Alonso some breathing space in terms of the pressure that would clearly have been on his shoulders from the get-go.
Of course, results are only one element of what will make his tenure successful, albeit a pretty major one.
The other issues that the manager needs to concern himself with are the dressing room, both in terms of the mix of characters within it, and keeping each and every player happy.
Dressing room balance has to be right
Of those two elements, the first should be achievable thanks to the fact that any incoming manager will have wanted to bring in his own players to shape the team both on and off the pitch, though signing ones who will upset the balance is a sure-fire way to disaster.
Assuming, therefore, that Alonso has the balance just right at present, it then comes down to how many players he has hammering on his door because they can't get a game.
Take the brilliant Estevao by way of example.
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Out of favour
The young Brazilian has bagged eight goals and three assists in his 38 games for the club so far, including one sumptuous strike in the Champions League against Barcelona.
Before injury cruelly ended his 2025/26 season early, he was looking every inch the player that Chelsea had thought they were buying, but since being sidelined, the club have now gone in a different direction by bringing Alonso in.
Reports in Brazil have already surfaced which suggest the player has confided to his inner circle that he doesn't believe he will get much playing time under the Spaniard, and will look to force the issue and leave in January if his assumptions prove correct.
His belief stems from the fact that his preferred playing position in the centre will now be taken by either Cole Palmer or Morgan Rogers, leaving Estevao to fight it out with Pedro Neto for the right-sided position.
Physicality could be an issue
For the 19-year-old to be a success there, he needs to be more physical, and arguably that isn't necessarily his forte.
Whilst he's already shown he's able to handle the physical aspects of the English game, he's not necessarily a player who likes to dish it out himself, and if Alonso prefers the two Englishmen centrally, as he has done so far in the Premier League, it does narrow Estevao's options if he isn't willing to play elsewhere.
Chelsea have shown before that they've no real loyalty to their players, with respect, and no one in the squad is safe from being sold if a deal is acceptable to the owners.
If Estevao believes by dropping hints in the media that he will get things his own way, he's likely to be sorely mistaken. There's also the issue of age.
Plenty of time to develop
As good as the Brazilian is, he still won't be 20 years of age until next April, so there really is plenty of time for him to develop into the player that Chelsea believed they would be getting when they spent £29m to secure him for the future when he was just 17 years of age.
Perhaps the player would do well to bear in mind that another talented South American, Lionel Messi, didn't really break through until he was about the same age as Estevao is now, and the Argentinian's development, certainly in his first season in the Barcelona first team, was taken slowly.
Xabi Alonso has already shown his nous as a manager and a coach, and there isn't too much doubt that he'll go on to be as successful in the dugout as he was on the pitch.
If he's keeping Estevao in reserve, there'll be a perfectly logical reason for that, and threats to leave because of lack of match time aren't going to sit well with the Spaniard.
Estevao would be far better advised to bide his time at Stamford Bridge and learn from one of the very best to have played the modern game.
When the youngster is primed and ready to take on the world, Alonso will be the first to let him do exactly that.
Far too many players nowadays want too much, too quickly, and Estevao needs to be mature enough to understand that unless he wants to risk becoming another statistic rather than a potential world-beater, his time on the sidelines will actually be time well spent.