If we take a look at Xanathar's Guide to Everything (201), we can see that they provide some advice for magic items, which we can then compare to the amount of gold our players receive. Generally, a common magic item costs around 40 gp, an uncommon one is around 300 gp, a rare one is around 11,000 gp, a very rare one is around 30,000 gp, and a legendary one is around 175,000 gp. This means that if a player saves every copper they get in a level 1-20 campaign, they won't be able to afford the legendary item until they receive one or two rolls for treasure level 17 or higher. One way to determine your starting gold is to get a gold fund and use it to buy your initial equipment.
Once your players reach Level 2, gold will start to lose its importance because it doesn't really matter how much gold they have. A character who retires at level 20 and has the average amount of gold and artwork thrown for them should retire with a total of 786,086 gold pieces. They start with their tier 1 gold according to their class, and then add the next gold based on their initial level. It only takes at least 10 gold a day to live like an Aristocrat, so you can throw all the gold you want at it.
The new character will have enough gold to buy competitive equipment, but will not dominate the other characters because gold can be spent to fit the setup perfectly.