A day before you plan to use the gin, start the infusion: To a large jar or airtight plastic container, add the gin, olive oil, rosemary, and thyme. Shake vigorously, then set aside at room temperature to infuse for 12 hours.
Transfer the jar to the freezer for another 12 hours (or overnight). This will cause the olive oil to solidify and separate. Place a fine mesh strainer over a second large jar or container, then strain the gin, discarding any solids. Wash and dry the original jar and the strainer then line the strainer with a coffee filter. Strain the gin once again to remove any remaining sediment and oil. Use immediately or cover tightly and use within 6 months.
Mix the olive oil martini: In a mixing glass filled with ice, add 2½ oz. of the infused gin gin, along with the vermouth and salt. Stir until well-chilled, then strain into a martini glass or coupe and garnish with as many olives as you like. Serve immediately.