Steady-state visual evoked potentials (SSVEP) brain-computer interface (BCI) provides reliable responses leading to high accuracy and information throughput. But achieving high accuracy typically requires a relatively long time window of one second or more. Various methods were proposed to improve sub-second response accuracy through subject-specific training and calibration. Substantial performance improvements were achieved with tedious calibration and subject-specific training; resulting in the user's discomfort. So, we propose a training-free method by combining spatial-filtering and temporal alignment (CSTA) to recognize SSVEP responses in sub-second response time. CSTA exploits linear correlation and non-linear similarity between steady-state responses and stimulus templates with complementary fusion to achieve desirable performance improvements. We evaluated the performance of CSTA in terms of accuracy and Information Transfer Rate (ITR) in comparison with both training-based and training-free methods using two SSVEP data-sets. We observed that CSTA achieves the maximum mean accuracy of 97.43$\pm$2.26 % and 85.71$\pm$13.41 % with four-class and forty-class SSVEP data-sets respectively in sub-second response time in offline analysis. CSTA yields significantly higher mean performance (p<0.001) than the training-free method on both data-sets. Compared with training-based methods, CSTA shows 29.33$\pm$19.65 % higher mean accuracy with statistically significant differences in time window less than 0.5 s. In longer time windows, CSTA exhibits either better or comparable performance though not statistically significantly better than training-based methods. We show that the proposed method brings advantages of subject-independent SSVEP classification without requiring training while enabling high target recognition performance in sub-second response time.