How early-stage platforms can overcome the chicken-and-egg problem is a central strategic challenge. We develop a dynamic model of two-sided platform adoption in which user utility depends on same-side and cross-side network effects, and adoption is shaped by advertising that increases sensitivity to perceived utility. We highlight the distinct role of advertising as a salience amplifier rather than a direct utility shifter. We derive closed-form conditions under which a platform takes off or collapses, showing that even when one side cannot sustain growth alone, targeted advertising on the other side can trigger self-reinforcing adoption. We show how advertising reduces the required strength of indirect network effects for critical mass and provides strategic guidance on where to allocate early marketing resources. To illustrate these mechanisms, we run agent-based simulations to illustrate the dynamics of three platform archetypes: marketplaces, service platforms, and ad-funded social networks. The simulations confirm that modest early advertising can reliably push the system past its critical threshold and that the optimal side to target depends on market size, the direction and strength of network effects, and competitive conditions within each side. We extend our model to incorporate competition between two platforms in which advertising can have spillovers (category versus brand advertising) and find that early differences in advertising levels across the platforms can tip the market towards one platform. We conclude with a discussion of managerial implications, giving actionable guidance for platform entrepreneurs to overcome the chicken-and-egg problem.