I work with people who have just taken on a puppy, so 3/4 days a week I am advising on how to raise, train, handle, dogs from 8 weeks to late adolescence... and I am a dog behaviourist, for context.
Don't do it.
A puppy takes to around 2 years, on average (small breeds a bit quicker, giant ones a bit slower) to stop being super mega needy and requiring you to compromise on your life in and out of your house.
Thats 2 years of hard work, prioritising their needs over your own and with children around too thats constantly juggling who needs what/when and the needs will often conflict. That inevitably means the dog is the one who misses out (and you) because the children are the priority. However a dog missing out on the training, enrichment, exercise and interaction they need = behaviour problems down the line.
With a rescue dog, if you get LUCKY it will be 6 months of settling in and training, chances are you won't because dogs sent to rescues are rarely steady older dogs without issues, they're usually early adolescents booted out of homes that did not have the time to see a dog through its adolescence.
So potentially a rescue dog is still a year or two of serious compromise to the lifestyle you actually want to lead.
Often people get very fixated on the image of the ideal, perfect, lovely adult dog who will lie in a basket quietly in the day (as my lovely perfect adult dogs are currently doing!) and be happy to pop out for a walk or a run, engage in a game or two in the back garden and then back to their basket. Thats pretty unrealistic even for a sensible adult dog but its pie in the sky for a young dog or a new rescue.
Every single shift at work, I'd say half the people I talk to got a dog/puppy they did not have time for, cannot make time for, and are building behaviour problems as a result of that lack of time - loving the dog and wanting the dog are not enough.
The end result unfortunately tends to be a dog being rehomed or sold on, and having missed out on the necessary input during their early months, means its much more likely they will lose the next home too...
Worst case scenario, children end up injured or.. worse.
If he really wants a dog and loves dogs, he'll be happy to wait until your youngest child is of an age to be somewhat independent, follow instructions reliably, be able to wait for a parents attention.
For some kids that might be 7 or 8. For some it might not be til 18+!