You can easily find out yourself. First use a black hole temperature calculator like

https://www.omnicalculator.com/physics/black-hole-temperatur...

or

https://www.vttoth.com/CMS/physics-notes/311-hawking-radiati...

to find the Hawking temperature T_BH of your black hole. Then use the fact that CMB temperature T_CMB is inversely proportional to the cosmological scale factor a(t), where t is time:

https://physics.stackexchange.com/questions/76241/cmbr-tempe...

Set a(t_now) = 1 for convenience; then

T_CMB(t) = T_CMB(t_now) / a(t)

and you want to find the time t when T_BH = T_CMB(t).

That depends on how the scale factor will change over time:

https://en.wikipedia.org/wiki/Scale_factor_(cosmology)

We don't know that, but if we assume for simplicity that dark energy will keep dominating, a(t) will grow exponentially, i.e.

a(t) = a(t) / a(t_now) ~ exp(H_0 * (t - t_now))

where H_0 is Hubble's constant. So

T_CMB(t) = T_CMB(t_now) / a(t) ~ T_CMB(t_now) / exp(H_0 * (t - t_now))

Numbers:

T_CMB(t_now) ~ 2.7 K

H_0 ~ 71 km/s/Mpc ~ 2.3e-18 s^-1

t_now ~ 14 Gyr ~ 3.2e16 s

so, with t expressed in seconds,

T_CMB(t) ~ 2.7 / exp(2.3e-18 * (t - 3.2e16)) K

Setting this equal to T_BH and solving for t, I get

t = 3.2e16 + ln(2.7 / T_BH) / 2.3e-18 s

So let's say you have a solar mass black hole. Then

T_BH ~ 6.16871e-8 K

and so

t ~ 7.7e18 s ~ 2.4e11 years

i.e. 240 billion years (17 times the current age of the universe).

That's actually not a humongous number, thanks to the exponential expansion of a(t). It would take a lot longer with the expansion rate of a matter-dominated universe (exercise for the reader!)