With almost 1.1 billion people lacking access to electricity, solar-based off-grid products like Solar Home Systems (SHS) have become a promising solution to provide basic electricity needs in un(der)-electrified regions. Therefore, optimal system sizing is a vital task as both oversizing and undersizing a system can be detrimental to system cost and power availability, respectively. This paper presents an optimal SHS sizing methodology that minimizes the loss of load probability (LLP), excess energy dump, and battery size while maximizing the battery lifetime. A genetic algorithm-based multi-objective optimization approach is utilized to evaluate the optimal SHS sizes. The potential for SHS to cater to every tier of the Multi-tier framework (MTF) for measuring household electricity access is examined. The optimal system sizes for standalone SHS are found for different LLP thresholds. Results show that beyond tier 2, the present day SHS sizing needs to be expanded significantly to meet the load demand. Additionally, it is deemed untenable to meet the electricity needs of the higher tiers of MTF purely through standalone SHS without compromising one or more of the system metrics. A way forward is proposed to take the SHS concept all the way up the energy ladder such that load demand can also be satisfied at tier 4 and 5 levels.