The main characters of the novel – Little Bee, Sarah, and Sarah's son Charlie – all walk a fine line between hope and desperation. Ultimately, these three find hope in each other, each providing what the others lack. Little Bee and Sarah also seem to find hope in continuing the work Andrew left behind (on the situation in Nigeria and the treatment of refugees in detention centers in the UK). Part of this continuation is collecting stories from other Nigerian people who experienced things like Little Bee did, in hopes of using them for a book meant to increase awareness of the situation. Little Bee and Sarah are not content to simply help themselves, but feel the need to assist others as well. Helping others might just be a crucial component of hope, at least according to Little Bee.
This connects the theme of hope with what author Chris Cleave says is a major theme: compassion (source). When characters are compassionate, and focus on soothing the suffering of others, their own desperation fades, at least momentarily. For example, at the end of the novel, Little Bee is so focused on helping Charlie live that she puts herself right in the hands of the soldiers who might want to kill her. Even though we don't know whether the characters survive the beach, the moment is hopeful in that it shows Little Bee performing acts of kindness toward Charlie, because it's the right thing to do, whatever the cost.