Sexual selection theory models evolution of sexual signals and preferences using simple life histories. However, life-history models predict that males benefit from increasing sexual investment approaching old age, producing age-dependent sexual traits. Age-dependent traits require time and energy to grow, and will not fully mature before individuals enter mating competition. Early evolutionary stages pose several problems for these traits. Age-dependent traits suffer from strong viability selection and gain little benefit from mate choice when rare. Few males will grow large traits, and they will rarely encounter choosy females. The evolutionary origins of age-dependent traits therefore remain unclear. I used numerical simulations to analyze evolution of preferences, condition (viability) and traits in an age-structured population. Traits in the model depended on age and condition ("good genes") in a population with no genetic drift. I asked (1) if age-dependent indicator traits and their preferences can originate depending on the strength of selection and the size of the trait; (2) which mode of development (age-dependent versus age-independent) eventually predominates when both modes occur in the population; and (3) if age-independent traits can invade a population with age-dependent traits. Age-dependent traits evolve under weaker selection and at smaller sizes than age-independent traits. Evolution of age-independent traits depends only on trait size, whereas evolution of age-dependent traits depends on both strength of selection and growth rate. Invasion of age-independence into populations with established traits followed a similar pattern with age-dependence predominating at small trait sizes. I suggest that reduced adult mortality facilitates sexual selection by favoring the evolution of age-dependent sexual signals under weak selection.