A log-rank test is a test of whether the hazard as a function of time differs between 2 groups. If the log-rank test doesn't show a significant difference between 2 curves in this respect, then you should be very reluctant to evaluate differences at specific survival times. That's a general principle of statistical tests: if the overall test isn't significant it's best to stop there. (The part of the question specific to how to do this in SPSS is off-topic on this site.)
That said, if you have a multiple-regression or other model that takes several covariates into account (generally a good idea in survival modeling), a log-rank test between 2 groups might not be informative if they differ in other covariate values. So if you have a more elaborate survival model than what you examined with your log-rank test, you certainly can examine survival estimates at specific times in the more elaborate model if it is significant overall.
In response to comment:
Unless you are examining a randomized controlled trial, trying to discern the actual effect of a treatment on outcome faces several problems. One good place to start learning about these issues is the freely available Causal Inference book by Hernán and Robins, which begins with simple, accessible situations and works up to analysis of complex longitudinal data sets with time-varying covariates and treatments.
There are several ways to try to adjust for differences in covariates between treatment groups. Otherwise, those differences between treatment groups could severely bias your estimate of the effect of treatment per se.
One way to approach this is a multiple regression that includes covariates associated with outcome as predictors. For survival analysis, this is often done with a Cox proportional hazards regression. See Harrell's Regression Modeling Strategies book or course notes for guidance in regression modeling.
Another way is to include or weight cases according to their probabilities, as a function of the covariates, of being in the treatment groups ("propensity scores," used for case matching or weighting). Those probabilities are often estimated by logistic regression, covered in the Harrell references.
Individually, those approaches require correctly specified models. As Hernán and Robins discuss, using both approaches together can provide a "doubly robust" assessment such that if either the regression or the propensity model is correct you can assess treatment-specific effects.
