Cloud infrastructure is managed through a mix of interfaces -- traditionally, cloud consoles, command-line interfaces (CLI), and SDKs are the tools of choice. Recently, Infrastructure-as-Code/IaC frameworks (e.g., Terraform) have quickly gained popularity. Unlike conventional tools, IaC~frameworks encode the infrastructure in a "source-of-truth" configuration. They are capable of automatically carrying out modifications to the cloud -- deploying, updating, or destroying resources -- to bring the actual infrastructure into alignment with the IaC configuration. However, when IaC is used alongside consoles, CLIs, or SDKs, it loses visibility into external changes, causing infrastructure drift, where the configuration becomes outdated, and later IaC operations may undo valid updates or trigger errors. We present NSync, an automated system for IaC reconciliation that propagates out-of-band changes back into the IaC program. Our key insight is that infrastructure changes eventually all occur via cloud API invocations -- the lowest layer for cloud management operations. NSync gleans insights from API traces to detect drift (i.e., non-IaC changes) and reconcile it (i.e., update the IaC configuration to capture the changes). It employs an agentic architecture that leverages LLMs to infer high-level intents from noisy API sequences, synthesize targeted IaC updates using specialized tools, and continually improve through a self-evolving knowledge base of past reconciliations. We further introduce a novel evaluation pipeline for injecting realistic drifts into cloud infrastructure and assessing reconciliation performance. Experiments across five real-world Terraform projects and 372 drift scenarios show that NSync outperforms the baseline both in terms of accuracy (from 0.71 to 0.97 pass@3) and token efficiency (1.47$\times$ improvement).