According to United States Forest Service, fire has a number of benefits for the wildlife including more nutrients in the ground, more open spaces, there are some plants that need fire to spread and it helps control invasive species.
Fire offers many benefits to wildlife and plant species. First and foremost, a fire is a natural process, unlike mowing or logging. Fire returns nutrients to the soil quickly, versus the years it takes for grass clippings, dead leaves, and logs to decompose and provide nutrients. In fact, it's not uncommon to see new growth within a few days of a fire!
Fire also opens up dense areas and helps maintain meadow habitats. Several animal species use these open areas for food and shelter. Birds such as bobolinks and eastern meadowlarks require open grasslands for feeding and resting. Mammals such as moose, deer, and rabbits rely on the new growth produced after a fire for food.
Fire also benefits several plant species such as the endangered sandplain gerardia and wood lily, both which need fire to reproduce and grow. The endangered Delmarva fox squirrel and red-cockaded woodpecker rely on fire to maintain their pine forest habitats.
Fire also helps control non-native invasive plant species. Non-native invasive plants are plants that have been introduced from another part of the world, and have "taken over" their new habitat. No matter where you live, chances are there is some type of invasive plant in your neighborhood. Here in the Northeast, common invasive plants include purple loosestrife, Japanese knotweed, common reed (aka Phragmites), and honeysuckle. Controlled burning can remove these invasive species from a particular area, allowing space for native plants to grow.
Source
There was also a more in depth study also done by the Forest Service which tracked the benefits to animals in areas that had been touched by fires. Whether or not fire increased or decreased the number of animals depended on the species of animal.
Deer and Elk
Deer summer-fall use (annuity value 1. 9) declined
the first year after fire, but then increased to levels
approaching 2.5 times the control through the rest of
the 20-year evaluation period (fig. 3). Deer winterspring
use also declined immediately following fire,
returned to the control level for a few years, and then
increased to levels exceeding 10 times that of the control.
..
For both trap periods, deer mice increased the first
year after fire, then declined to the level of the control
at 7 years. After 7 years, there was another increase to
2.5 times the control level in the summer, and 6 times
the control level in the spring. Annuities were 1.8 and
3.3 for summer and spring, respectively
...
Total bird
numbers (annuity value 0.71) increased the first year
after fire, then decreased to below the prefire level for
the remainder of the evaluation period
Source
I found another study which went through and listed the benefits for each species and it looks like some species benefit and others do not, depending on the species and type of fire.
Pedersen et al.
(2003) modelled effects of fire and concluded that small
fires may benefit sage-grouse, but large fires (>10% of the
spring-use area) occurring at high frequencies (17 years
between fires) could result in their extirpation.
...
Fire is important to pronghorn because it
creates the desired density of grasses and forbs and
improves quality of forbs for foraging (Yoakum 2004).
Fire can also maintain shrub cover at desirable densities
and heights for pronghorn
...
At the species level, however, western
bluebirds benefitted from severe- and moderate-fire, whitebreasted
and pygmy nuthatches benefitted by moderate-fire,
but mountain chickadees were negatively affected by any
fire.
Source
As you wanted to know what the timelines were, I would suggest the charts starting on page 5 of this study.
If you are looking for more information, I would suggest these resources,
