That depends on how well connected it is.
If it has a direct connection to the mining pool that solves the block, then your full node will hear about the block as soon as (or sooner than) any other blockchain explorer website.
If it does not have a direct connection to the mining pool that solves the block, then it could take as much as a few seconds (depending on just how many connections the block has to pass through before it gets to you and how fast those connections relay the block).
Unless you make a specific effort to configure your full bitcoin node to have a direct connection to all (or most) of the major mining pools, I'd expect your average time to be somewhere between those extremes. Sometimes you'll get it a fraction of a second after the blockchain explorer site, and sometimes you'll get it at the same time (or maybe a fraction of a second before if they aren't well connected at that moment.
Oh okay, if it's only a few seconds at the most then that's perfect. I was thinking that it may end up being like a minute.
If you have a poor latency to your peers, then you'll probably experience significant delays. Block headers are fairly small to relay and can be relayed first before the block itself so bandwidth is no issue there if you only want to be notified of the latest block. As mentioned, the timing would vary depending on how many hops a specific block take before it reaches the target node and it would vary from time to time.
You also have to factor in the latency between the block explorer if you want to get your data from there. Here's a few blocks that I have compiled between two nodes that are fairly far apart, geographically. Interestingly, the difference is only 2 seconds but there's definitely insufficient sample size. Unfortunately, I'm unable to compare this to the Blockchair as they seem to be using Median time which doesn't reflect the actual time received.
Home Node: 2021-03-13T04:42:27Z UpdateTip: new best=0000000000000000000086661c2e8852a683d62aef5712d29e91918041c1f844 height=674386 version=0x20400000 log2_work=92.731396 tx=624319389 date='2021-03-13T04:42:17Z' progress=1.000000 cache=311.2MiB(2310354txo)
Dedicated Node: 2021-03-13T04:42:25Z UpdateTip: new best=0000000000000000000086661c2e8852a683d62aef5712d29e91918041c1f844 height=674386 version=0x20400000 log2_work=92.731396 tx=624319389 date='2021-03-13T04:42:17Z' progress=1.000000 cache=200.4MiB(116>
Home node: 2021-03-13T04:41:52Z UpdateTip: new best=000000000000000000091afc491f67dc650c37b33bdbacb2a5dd284d01090f00 height=674385 version=0x20000000 log2_work=92.731380 tx=624319194 date='2021-03-13T04:41:56Z' progress=1.000000 cache=310.4MiB(2304030txo)
Dedicated Node: 2021-03-13T04:41:50Z UpdateTip: new best=000000000000000000091afc491f67dc650c37b33bdbacb2a5dd284d01090f00 height=674385 version=0x20000000 log2_work=92.731380 tx=624319194 date='2021-03-13T04:41:56Z' progress=1.000000 cache=200.4MiB(116>
Home node: 2021-03-13T04:39:49Z UpdateTip: new best=00000000000000000001a00e6957773a5191493353f553249c0d97d8b2ffbadd height=674384 version=0x20000000 log2_work=92.731364 tx=624318828 date='2021-03-13T04:39:27Z' progress=1.000000 cache=309.6MiB(2297496txo)
Dedicated Node: 2021-03-13T04:39:47Z UpdateTip: new best=00000000000000000001a00e6957773a5191493353f553249c0d97d8b2ffbadd height=674384 version=0x20000000 log2_work=92.731364 tx=624318828 date='2021-03-13T04:39:27Z' progress=1.000000 cache=200.3MiB(116>
I plan on using an OVH VPS to host the bitcoin node, so hopefully the latency should be good enough.
The block explorer doesn't matter too much for me, since I'll only be using it to get general information about unconfirmed transactions, such as the time they was first seen and the fee that they're using.
Thanks for the help both of you