NEW DELHI—Apple is preparing to manufacture its new iPhone in India months earlier than it did previous models, a sign the company is boosting production outside its traditional base of China, where Covid-related shutdowns and geopolitical tensions have raised risks for foreign businesses. Apple has been working with contract manufacturers in India to speed up the production process, shortening the typical delay between when the devices are made in China and when they are produced in the South Asian nation, according to people familiar with the matter.