Population genetic studies in tropical plants are often challenging because of limited information on taxonomy, phylogenetic relationships and distribution ranges, scarce genomic information and logistic challenges in sampling. We describe a strategy to develop robust and widely applicable genetic markers based on a modest development of genomic resources in the ancient tropical tree species Symphonia globulifera L.f. (Clusiaceae), a keystone species in African and Neotropical rainforests. We provide the first low‐coverage (11X) fragmented draft genome sequenced on an individual from Cameroon, covering 1.027 Gbp or 67.5% of the estimated genome size. Annotation of 565 scaffolds (7.57 Mbp) resulted in the prediction of 1046 putative genes (231 of them containing a complete open reading frame) and 1523 exact simple sequence repeats (SSRs, microsatellites). Aligning a published transcriptome of a French Guiana population against this draft genome produced 923 high‐quality single nucleotide polymorphisms. We also preselected genic SSRs in silico that were conserved and polymorphic across a wide geographical range, thus reducing marker development tests on rare DNA samples. Of 23 SSRs tested, 19 amplified and 18 were successfully genotyped in four S. globulifera populations from South America (Brazil and French Guiana) and Africa (Cameroon and São Tomé island, FST = 0.34). Most loci showed only population‐specific deviations from Hardy–Weinberg proportions, pointing to local population effects (e.g. null alleles). The described genomic resources are valuable for evolutionary studies in Symphonia and for comparative studies in plants. The methods are especially interesting for widespread tropical or endangered taxa with limited DNA availability.