Learn Russian: Я смогу победить эту изоляцию.

The verb победить (to defeat/win) is a classic 'defective verb'. It doesn't have a 1st-person singular form in the future tense—there is no such word as я побежу or я победю. To express 'I will defeat', you must use a workaround. Adding смогу (I will be able to) before the infinitive is one of the most natural ways to solve this.

Could I use the future tense of the imperfective form, like я буду побеждать, to avoid this problem?

You could, but it changes the meaning. Побеждать is imperfective, so я буду побеждать means 'I will be defeating' or 'I will be winning' on a regular, ongoing basis. Here, the speaker wants to talk about a single, completed victory over this specific isolation, so a perfective workaround is required.

Since победить lacks an 'I' form, does it lack forms for 'you' or 'they' as well?

No, it is only defective for я (I). The rest of the future tense conjugation works perfectly normally. You can freely say ты победишь (you will defeat), она победит (she will defeat), and мы победим (we will defeat).

What is another common workaround if I don't want to use смогу (will be able to)?