Tree based genetic programming (GP) traditionally uses simple S-expressions to represent programs, however more expressive representations, such as lambda calculus, can exhibit better results while being better suited for typed GP. In this paper we present population initialization methods within a framework of GP over simply typed lambda calculus that can be also used in the standard GP approach. Initializations can be parameterized by different search strategies, leading to wide spectrum of methods corresponding to standard ramped half-and-half initialization on one hand, or exhaustive systematic search on the other. A novel geometric strategy is proposed that balances those two approaches. Experiments on well known benchmark problems show that the geometric strategy outperforms the standard generating method in success rate, best fitness value, time consumption and average individual size.