You’ve seen the pictures. Dust exploding as thousands of wildebeest thunder across the plains. Crocodiles lurking in the rivers. Lions along the banks stalking a moveable feast. The great migration – the annual 2,800km circuit of millions of wildebeest and zebra traversing Tanzania’s Serengeti National Park and Kenya’s Masai Mara – is one of the world’s more spectacular shows, especially in autumn, when the herds make their dramatic crossing of the Mara River in the Serengeti’s north. But like all hot tickets, the autumn migration can come with its share of hassles, including sky-high prices and traffic jams as safari vehicles jostle for space near the best sightings.

But from January through March – the Serengeti’s green season – approximately 1.5 million wildebeest graze along the vast plains of Tanzania’s southern Serengeti, feeding on the grasses that spring from late autumn’s rains and giving birth to their young. This allows travellers a chance to get a sneak peek of the migration down south before indulging in the crowd-free wildlife show of the north. So I set off in early February to check out the Serengeti’s lesser known green season.

Our tiny plane touched down in the dirt of the Ndutu airstrip in the Serengeti’s south, a staging zone for the mobile safari outfitters that follow the great migration. These moveable camps spend the winter months in this area before following the herds up to the western Serengeti by spring and then onto the north during the late summer and early autumn (the most popular time to see the migration as it thunders across the dramatic river crossings.

As our Land Cruiser sped off down toward the nine-tent Olakira Camp, the sheer scale of the landscape unfolded, the spiny flat-tops of the acacia trees dotting undulating fields of grass and gentle hills rolling out to wide open vistas of scruffy brush. In the Maasai language, Serengeti means “extended place” or “endless plains”. You almost need a backdrop of such excess to wrap your head around the incredible amount of wildlife here. A pride of ostriches sped past a herd of wildebeest tending to their newborns. An aptly named dazzle of zebra massed its graphic stripes into a psychedelic backdrop for mongooses moving as one organism, scurrying and popping up, scurrying and popping up again.

As the sun set, Maasai guards lit a path from our tent to a campfire surrounded by flickering lanterns. Wisps of pink clouds obscured a pearlescent moon as guests lingered over dinner, swapping stories of the day’s adventures – a lion took down a pregnant wildebeest, a baby leopard was spotted in the fork of a tree. Then we were escorted back to the tents, hot water bottles already warming the soft, king-sized sheets (with hot showers, flush toilets and colonial-inspired furniture, you are far from roughing it here).

From my cosy cocoon, I heard the call and response of birds zipping electrically through the night air, the staccato rhythm of galloping hooves, the whoop of hyenas stalking fresh meat. A light rain pattered on the canvas roof, crescendoing to a dramatic downpour that eventually lulled me to sleep. It also left a present for the morning: a perfect rainbow arched over a saturated sunrise of peach and crimson.

Staying so close to nature (as opposed to being tucked away in a traditional lodge) lulls you into the rhythms of the bush, awakening with the sun, greeting the animals’ morning activity on a game drive, napping when the sun burns too bright. It also means expecting the unexpected, like, perhaps, a terrifying guttural roar directly outside your tent, a lion so close you can hear his soft feet padding the dust just beyond the canvas.

Though we didn’t see as many wildebeest herds as we would have liked (the migration is unpredictable and we missed much of the main movement), there was no lack of game. Cresting a hill, we saw six giraffe lope across an emerald basin. We stalked a cheetah hunting to feed its young. As the sun hung heavy in the sky, we descended into a valley to find four napping lionesses guarded by two fierce males, their wild manes glowing orange, then amber as the sun set.

After three days of game drives, we were ready to make our own migration north, boarding a prop plane to Lamai in the northern Serengeti. Since the migration will not make its way up here until autumn, it was blissfully empty of other travellers. There are just 54 permanent beds here compared with more than 9,000 in a similarly sized area of Kenya’s Maasai Mara. And though most of the wildebeest have yet to arrive, other animals crowd the plains.

Not five minutes after landing we were on the banks of the Mara River, flanked by 6m-long crocodiles and hundreds of hippos wallowing in the shallows. Then we crested a hill, plunging into a sea of oat grass as high as our 4x4. In the distance, a straggling herd of wildebeest arced up and back into the grass like dolphins leaping from the water. Another corner, another 10 minutes and it was zebra among buffalo among ostriches among giraffes, with lilac breasted rollers soaring overhead.

The 12-room Nomad Tanzania's Lamai Serengeti has a front-row seat to the show. Set atop Kogakuria Kopje, a boulder-strewn hill, the plains unfold dramatically below. From the whitewashed villas you can survey elephants crossing the plain. Swahili day beds piled with hand-woven pillows and draped with romantic netting front wooden balconies, all with similarly cinematic views.

In the south (and in most of Tanzania’s game reserves), water is scarce so predators lurk at the watering holes, ready to pick off thirsty antelope, zebra and wildebeest. The prevalence of water in the north, however, spreads out the game: you will often find big cats perched dramatically atop red rock outcrops, the better to spot prey. After days tracking herds of elephants across rivers, seeing two leopards hunt in the tall grasses and spotting two endangered white rhino – I felt sated, lucky, spoiled by this natural bounty. As the sky darkened and storm clouds gathered on the horizon, our jeep turned towards home. Suddenly a flash of fur, a low growl, and a leopard sprung across our path, leaping atop a hulking solitary boulder. It crouched there, a tightly wound spring scanning the horizon for prey, all lean muscle, tense sinews against the roiling clouds. I could barely breathe as its head jutted forward, teeth bared, eyes trained on some far off movement. Then as fast as it started, it was over; the antelope got away and the cat flopped down to rest. It was time to head home.