One of the mains challenges of biosemiotics is ‘to attempt to naturalize biological meaning’ [Sharov & all 2015]. That challenge brings to look at a possible evolutionary thread for biosemiotics based on meaning generation for internal constraint satisfaction, starting with a pre-biotic entity emerging from a material universe. Such perspective complements and extends previous works that used a model of meaning generation for internal constraint satisfaction (the Meaning Generator System) [Menant 2003a, b; 2011]. We propose to look at such an evolutionary thread for biosemiotics in three steps. The first step presents the proposed emergence of a pre-biotic entity as a far from thermodynamic equilibrium volume constrained to maintains its status [Menant 2015]. Such constraint dependence introduces natural links with teleology and with meaning generation. It also introduces perspectives for evolutionary origins of agency, self, and autonomy, coming in addition to other biosemiotic perspectives [Tønnessen, 2015]. The next step recalls the MGS as being a system approach linking the agent containing it to its environment and bringing to the agent a control from within. We apply the MGS to animal life. Relations with the Umwelt, with constructivism and with the Peircean triadic approach are highlighted. The last step of the thread brings the evolution of life up to humans where specificities related to human mind have to be taken into account. Among them is self-consciousness for which an existing evolutionary scenario introduces anxiety management as a foundational human constraint [Menant, 2014]. We link that scenario to the evolutionary thread because it introduces specific human constraints and is based on the evolution of meaningful representations. A conclusion summarizes the steps of the proposed evolutionary thread. More work is needed on that subject. Possible continuations are introduced.