Preheat the oven to 325°F (165°C), with a rack in the middle. Set an 8-inch round metal cake pan inside a larger roasting pan. Have your ingredients measured before starting the caramel.
Combine the sugar and water in a small heavy-bottomed saucepan. Stir gently to moisten the sugar, then cook over medium heat without stirring until the syrup turns a clear amber color, approximately 8–12 minutes. Gently swirl the saucepan if the color develops unevenly.
Immediately pour the caramel into the cake pan. Wearing oven mitts, carefully tilt the pan to coat the bottom. Set aside while preparing the custard. The caramel will harden; this is normal.
Measure 1/2 cup of the evaporated milk into a small microwave-safe bowl. Warm it briefly until warm but not boiling. Stir in the instant espresso powder until dissolved, then let it cool until lukewarm.
In a large bowl, gently whisk the eggs just until combined. Whisk in the sweetened condensed milk, remaining evaporated milk, cooled coffee mixture, vanilla, and salt. Mix until smooth without whipping in excessive air.
Pour the custard through a fine-mesh strainer into the caramel-lined pan. Cover the flan pan snugly with aluminum foil.
Place the roasting pan on the oven rack. Carefully pour hot water into the roasting pan until it reaches halfway up the outside of the flan pan, keeping water out of the custard.
Bake for approximately 60–75 minutes, checking at 55 minutes. The edges should be set, and the center should tremble gently as one piece when the pan is nudged. It should not ripple or slosh like liquid. If needed, continue baking in 5-minute increments.
Carefully lift the flan pan out of the water bath and place it on a wire rack. Remove the foil and cool for about 1 hour. Cover and refrigerate for at least 4 hours, preferably overnight.
To unmold, run a thin knife around the inside edge of the pan. Place a large rimmed platter over the pan, hold both firmly, and invert in one confident motion. Wait briefly for the flan to release before lifting the pan.
Spoon the released caramel around the flan. Cut into 8 slices and serve chilled.