Don’t worry, this is a common problem.
Temperature is absolutely vital when making a martini. Ideally the gin should be stored in the freezer for at least 8 hours prior to use. I keep it there all the time. I keep the glasses in there too.
Have you squeezed lemon peel into the glass? This isn’t just a gimmick. The fresh flavour helps cut through the alcohol.
Finally, for beginners or even seasoned drinkers, there’s nothing wrong with ordering or making a martini which uses sweet vermouth instead of dry. Martini bianco is absolutely fine for this and really takes the edge off the drink.
Anyone who complains that this is not a real martini should look back at the history of the drink. Originally all martinis were reportedly made with sweet vermouth.
Additionally, for more regular martini drinkers. I find that if you use sweet vermouth instead of dry vermouth you can actually use less of it, and therefore have more gin, providing you with a stronger drink that allows you to taste the gin with more purity.
Some experts have sniffed at this notion but I have tried and tested it numerous, numerous times on a wide range of drinkers with various experience levels and the results were almost completely unanimous. So there you go.
So, in summary, if you think martinis taste too strong for you, make sure the gin is cold enough, don’t skip the lemon peel, consider drinking it “dirty” and try mixing it with sweet vermouth instead of dry.