user5380: In Buddhism, we believe in rebirth and karma. But was there a time when it was our first time in any of the 31 Planes of Existence? 
If that is the case, how would we be reborn anywhere since we did not have any karma to pay off?
If that is not the case, how were we just infinitely here?

user2282: From the Buddha's famous "Tears" sutta:

At Savatthi. There the Blessed One said: "From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on. What do you think, monks: Which is greater, the tears you have shed while transmigrating & wandering this long, long time — crying & weeping from being joined with what is displeasing, being separated from what is pleasing — or the water in the four great oceans?"
"As we understand the Dhamma taught to us by the Blessed One, this is the greater: the tears we have shed while transmigrating & wandering this long, long time — crying & weeping from being joined with what is displeasing, being separated from what is pleasing — not the water in the four great oceans."

So,

If that is not the case, how were we just infinitely here?

We're still here simply because our "fuel" (greed/anger/delusion) is still here. If the fuel's still here, the machine will keep on running. No more fuel means no more wandering in samsara.

user-1: If i may kindly correct the beginning sentence of your question, i.e. "In Buddhism, we believe in rebirth and karma."
We actually try to verify these things for ourselves by studying reality through insight meditation, thereby gaining insights into how reality functions. We practice to gain experiental knowledge instead of believing things to be in a certain way.
Through insight meditation one will come to see that phenomena arise dependent on causes and conditions. One sees that phenomena can spawn new phenomena.
Looking for a first cause is problematic. Why is that?
A first cause breaks causality. One can then ask "What caused the first cause? Or What caused the cause that caused the first cause? And so on ad infinitum".
This question of origin also belongs to The Four Imponderables, namely the 4th one "Speculation about [the origin, etc., of] the cosmos is an imponderable that is not to be speculated about".
The Buddha explained that is it not conducive to ones practice to think about these things. That is because one cannot understand it unless one is a Buddha. If one is not a Buddha thinking about them will only leave the mind agitated and distressed which will not be beneficial for ones practice.

"Therefore, o monks, do not brood over [any of these views] Such brooding, O monks, is senseless, has nothing to do with genuine pure conduct (s. ādibrahmacariyaka-sīla), does not lead to aversion, detachment, extinction, nor to peace, to full comprehension, enlightenment and Nibbāna."
-- SN 56: Saccasamyutta.


5380: <p>In Buddhism, we believe in rebirth and karma. But was there a time when it was our first time in any of the <a href="http://www.accesstoinsight.org/ptf/dhamma/sagga/loka.html">31 Planes of Existence?</a> </p>

<p>If that is the case, how would we be reborn anywhere since we did not have any karma to pay off?</p>

<p>If that is not the case, how were we just infinitely here?</p>
 2282: <p>From the Buddha's famous <a href="http://www.accesstoinsight.org/tipitaka/sn/sn15/sn15.003.than.html" rel="nofollow noreferrer">&quot;Tears&quot; sutta</a>:</p>
<blockquote>
<p>At Savatthi. There the Blessed One said: &quot;From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating &amp; wandering on. What do you think, monks: Which is greater, the tears you have shed while transmigrating &amp; wandering this long, long time — crying &amp; weeping from being joined with what is displeasing, being separated from what is pleasing — or the water in the four great oceans?&quot;</p>
<p>&quot;As we understand the Dhamma taught to us by the Blessed One, this is the greater: the tears we have shed while transmigrating &amp; wandering this long, long time — crying &amp; weeping from being joined with what is displeasing, being separated from what is pleasing — not the water in the four great oceans.&quot;</p>
</blockquote>
<p>So,</p>
<blockquote>
<p>If that is not the case, how were we just infinitely here?</p>
</blockquote>
<p>We're still here simply because our &quot;fuel&quot; (greed/anger/delusion) is still here. If the fuel's still here, the machine will keep on running. No more fuel means no more wandering in samsara.</p>
 -1: <p>If i may kindly correct the beginning sentence of your question, i.e. <em>&quot;In Buddhism, we believe in rebirth and karma.&quot;</em></p>
<p>We actually try to verify these things for ourselves by studying reality through insight meditation, thereby gaining insights into how reality functions. We practice to gain experiental knowledge instead of believing things to be in a certain way.</p>
<p>Through insight meditation one will come to see that phenomena arise dependent on causes and conditions. One sees that phenomena can spawn new phenomena.</p>
<p>Looking for a first cause is problematic. Why is that?</p>
<p>A first cause breaks causality. One can then ask <em>&quot;What caused the first cause? Or What caused the cause that caused the first cause? And so on ad infinitum&quot;</em>.</p>
<p>This question of origin also belongs to <a href="https://en.wikipedia.org/wiki/Acinteyya" rel="nofollow noreferrer">The Four Imponderables</a>, namely the 4th one <em>&quot;Speculation about [the origin, etc., of] the cosmos is an imponderable that is not to be speculated about&quot;</em>.</p>
<p>The Buddha explained that is it not conducive to ones practice to think about these things. That is because one cannot understand it unless one is a Buddha. If one is not a Buddha thinking about them will only leave the mind agitated and distressed which will not be beneficial for ones practice.</p>
<blockquote>
<p>&quot;Therefore, o monks, do not brood over [any of these views] Such brooding, O monks, is senseless, has nothing to do with genuine pure conduct (s. ādibrahmacariyaka-sīla), does not lead to aversion, detachment, extinction, nor to peace, to full comprehension, enlightenment and Nibbāna.&quot;</p>
<p>-- SN 56: Saccasamyutta.</p>
</blockquote>
