Absolutely! These topics are all over the history of philosophy, and are found in most religions as well. However, most solutions tend to be different than existentialism itself (and the tone is often different). I'll only survey a couple attempts here, because these worries- how to live a meaningful life and avoid suffering, form one of the core subject matters of Ethics itself.

Ancient Greek philosophy was very concerned with the idea of how to live a good life and what gave life meaning. The works of Plato, the Stoics, Pyrrhonists, and Epicureans were all concerned (perhaps even primarily so) with how to live a meaningful life and cope with suffering.

For instance, the Epicureans were interested in the fear of death and suffering, writing extensively on the topics. For one of my favorite Epicurean takes on these topics you can see the Roman author Lucretius's De rerum natura or On the nature of things. Epicureans stressed living of a moderate life and to take joy in the pleasures of life while not allowing pains to disturb us. Another good text for these hellenistic philosophies is "The Post Socratics Vol. I" by Long and Sedley.

The lack of self and the death of the ego (and embracing the impermanence of all things) is a key concept in Buddhist philosophy. Buddhism sees the root of all suffering as the attachment of an illusory self to impermanent things. Only when we come to accept impermanence and to rid ourselves of the notion of the self can we avoid this suffering and escape the world of rebirth and impermanence. Obviously the key work in Buddhism is the Dhammapada, though for a layperson directed take on the religion I like "The heart of Buddha's Teaching" by Thich Nhat Hanh. Though note this latter is a religious text, not an academic source. It does however convey the Buddhist method of combating existential considerations.

One also finds such themes in the bible, the book of Job comes to mind (though this also deals with the problem of Evil), though I'm no expert on biblical philosophy to point to exact chapters.

For intros to other considerations see these videos by professional philosophers.

Edit- one thing I thought I would add is that the existentialists seem to have such a unique approach to these questions primarily because they were responding to the failure of many of these ethical systems (at least in their minds). Thinkers in the industrial era suddenly found themselves with the arguments for God undermined, completely physical explanations of the world, and even more importantly physical explanations of the person, which led to a distinctively pessimistic view of these questions.