A platform trial is a trial involving an innovative adaptive design with a single master protocol to efficiently evaluate multiple interventions. It offers flexible features such as dropping interventions for futility and adding new interventions to be evaluated during the course of a trial. Although there is a consensus that platform trials can identify beneficial interventions with fewer patients, less time, and a higher probability of success than traditional trials, there remains debate on certain issues, one of which is whether (and how) the non-concurrent control (NCC) (i.e., patients in the control group recruited prior to the new interventions) can be combined with the current control (CC) in the analysis, especially if there is a change of standard of care during the trial. Methods: In this paper, considering time-to-event endpoints under the proportional hazard model assumption, we introduce a new concept of NCC concurrent observation time (NCC COT), and propose to borrow NCC COT through left truncation. This assumes that the NCC COT and CC are comparable. If the protocol does not prohibit NCC patients to change the standard of care while on study, NCC COT and CC likely will share the same standard of care. A simulated example is provided to demonstrate the approach. Results: Using exponential distributions, the simulated example assumes that NCC COT and CC have the same hazard, and the treatment group has a lower hazard. The estimated HR comparing treatment to the pooled control group is 0.744 (95% CI 0.575, 0.962), whereas the comparison to the CC group alone is 0.755 (95% CI 0.566, 1.008), with corresponding p-values of 0.024 versus 0.057, respectively. This suggests that borrowing NCC COT can improve statistical efficiency when the exchangeability assumption holds. Conclusion: This article proposes an innovative approach of borrowing NCC COT to enhance statistical inference in platform trials under appropriate scenarios.