Typically, in toy models of kinematics, time isn't taken into account when calculating friction.
In the equation Fsmax = mu_s × Fn (maximum static friction equals coefficient of static friction times normal force of object), either the static friction benchmark is met or it isn't—time just isn't taken into account.
Realistically, friction isn't ideal. Generally, static friction is the result of opposing grooves and imperfections between contacting surfaces on a smaller, microscopic scale. Think of interlocking mechanical teeth, but a lot less orderly. Each microscopic ridge and groove is made up of structures that are subject to warping under mechanical stress or heat due to compression.
Realistically, you would not need to wait infinite time before an object overcomes static friction because of this.
Ultimately, most particles are expected to decay.