I'm trying to make an animation but in the initial frame the subsurface is generating these black lines and I don't know how to remove them.

Then the animation is ok but when they are all together it generates these black lines.

I'm using Karma GPU Solaris + Houdini 20.5

SS does not handle internal Split edges as a whole, there will always be dark/colored stripes.
In general, SS in Karma is so bad that it requires a separate question - does SideFx plan to improve it. It seems to me that it is better not to enable SS at all now.

This is a problem inherent in random walk-based SSS (the walk hits the internal face, and when tries to evaluate light on it, it's fully in shadow). You can reduce this type of artifacts by increasing SSS limit property (via rendergeometrysettings LOP), which allows the walk to continue from the points in shadow.

Old-fashioned diffusion approximation SSS sidesteps this issue but keep in mind it requires vex-based material and thus won't work under XPU.