I first just tried getting the two-transistor astable multivibrator to work in ltspice and here's what I had to do:
1. Use a real transistor model (e.g. 2n2222) instead of the generic one
2. Specify an initial condition on one of the caps
3. Add the "uic" option to the transient analysis directive.
#2 disrupts the symmetry in the circuit so that it will start to oscillate.
To set the initial voltage on a cap see this post:
https://www.eevblog.com/forum/beginners/ltspice-what-does-ic-v(c1)10-actually-do/msg5497798/#msg5497798or you can set the initial voltage of a node on one side of the cap using the
.IC V(...)=... directive.
Another way to disrupt the symmetry is to make one of the cap values slightly different from the other.
Note that the .asc file attached below is flawed in that it attempts to set the initial cap voltage using
.IC V(C1)=... which seems to be quietly ignored by ltspice.
... and the LTspice file is available here.
It's better to upload the asc file as part of your post.